Image-forming optical system

ABSTRACT

A high-performance image-forming optical system made compact and thin by folding an optical path using reflecting surfaces arranged to minimize the number of reflections. The image-forming optical system has a single prism. When image-side three surfaces of the prism are defined as a surface A, a surface B and a surface C in order from the image plane side thereof, at least one of the surfaces B and C has a rotationally asymmetric curved surface configuration that gives a power to a light beam and corrects aberrations due to decentration. The optical system leads light rays from an object to the image plane without forming an image in the prism and has a pupil in the prism. The surface A is a transmitting surface through which rays exit from the prism. The surfaces B and C are internally reflecting surfaces, which are positioned to face each other to form a Z-shaped optical path.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to image-forming optical systems.More particularly, the present invention relates to a decentered opticalsystem with a reflecting surface having a power for use in opticalapparatus using a small-sized image pickup device, e.g. video cameras,digital still cameras, film scanners, and endoscopes.

[0002] Recently, with the achievement of small-sized image pickupdevices, image-forming optical systems for use in video cameras, digitalstill cameras, film scanners, endoscopes, etc. have also been demandedto be reduced in size and weight and also in cost.

[0003] In the general rotationally symmetric coaxial optical systems,however, optical elements are arranged in the direction of the opticalaxis. Therefore, there is a limit to the reduction in thickness of theoptical systems. At the same time, the number of lens elementsunavoidably increases because it is necessary to correct chromaticaberration produced by a rotationally symmetric refracting lens used inthe optical systems. Therefore, it is difficult to reduce the cost inthe present state of the art. Under these circumstances, there haverecently been proposed optical systems designed to be compact in size bygiving a power to a reflecting surface, which produces no chromaticaberration, and folding an optical path in the optical axis direction.

[0004] Japanese Patent Application Unexamined Publication (KOKAI) Number[hereinafter referred to as “JP(A)”] 7-333505 proposes to reduce thethickness of an optical system by giving a power to a decenteredreflecting surface and thus folding an optical path. In an examplethereof, however, the number of constituent optical members is as largeas five, and actual optical performance is unclear. No mention is madeof the configuration of the reflecting surface.

[0005] JP(A) 8-292371, 9-5650 and 9-90229 each disclose an opticalsystem in which an optical path is folded by a single prism or aplurality of mirrors integrated into a single block, and an image isrelayed in the optical system to form a final image. In theseconventional examples, however, the number of reflections increasesbecause the image is relayed. Accordingly, surface accuracy errors anddecentration accuracy errors are transferred while being added up.Consequently, the accuracy required for each surface becomes tight,causing the cost to increase unfavorably. The relay of the image alsocauses the overall volumetric capacity of the optical system to increaseunfavorably.

[0006] JP(A) 9-222563 discloses an example of an optical system thatuses a plurality of prisms. However, because the optical system isarranged to relay an image, the cost increases and the optical systembecomes large in size unfavorably for the same reasons as stated above.

[0007] JP(A) 9-211331 discloses an example of an optical system in whichan optical path is folded by using a single prism to achieve a reductionin size of the optical system. However, the optical system is notsatisfactorily corrected for aberrations.

[0008] JP(A) 8-292368, 8-292372, 9-222561, 9-258105 and 9-258106 alldisclose examples of zoom lens systems. In these examples, however, thenumber of reflections is undesirably large because an image is relayedin a prism. Therefore, surface accuracy errors and decentration accuracyerrors of reflecting surfaces are transferred while being added up,unfavorably. At the same time, the overall size of the optical systemunavoidably increases, unfavorably.

[0009] JP(A) 10-20196 discloses an example of a two-unit zoom lenssystem having a positive front unit and a negative rear unit, in whichthe positive front unit comprises a prism of negative power placed onthe object side of a stop and a prism of positive power placed on theimage side of the stop. JP(A) 10-20196 also discloses an example inwhich the positive front unit, which comprises a prism of negative powerand a prism of positive power, is divided into two to form a three-unitzoom lens system having a negative unit, a positive unit and a negativeunit. However, the prisms used in these examples each have twotransmitting surfaces and two reflecting surfaces, which are allindependent surfaces. Therefore, a relatively wide space must be ensuredfor the prisms. In addition, the image plane is large in size inconformity to the Leica size film format. Accordingly, the prismsthemselves become unavoidably large in size. Furthermore, because thedisclosed zoom lens systems are not telecentric on the image side, it isdifficult to apply them to image pickup devices such as CCDs. In eitherof the examples of zoom lens systems, zooming is performed by moving theprisms. Accordingly, the decentration accuracy required for thereflecting surfaces becomes tight in order to maintain the requiredperformance over the entire zooming range, resulting in an increase inthe cost.

[0010] When a general refracting optical system is used to obtain adesired refracting power, chromatic aberration occurs at an interfacesurface thereof according to chromatic dispersion characteristics of anoptical element. To correct the chromatic aberration and also correctother ray aberrations, the refracting optical system needs a largenumber of constituent elements, causing the cost to increase. Inaddition, because the optical path extends straight along the opticalaxis, the entire optical system undesirably lengthens in the directionof the optical axis, resulting in an unfavorably large-sized imagepickup apparatus.

[0011] In decentered optical systems such as those described above inregard to the prior-art, an imaged figure or the like is undesirablydistorted and the correct shape cannot be reproduced unless the formedimage is favorably corrected for aberrations, particularly rotationallyasymmetric distortion.

[0012] Furthermore, in a case where a reflecting surface is used in adecentered optical system, the sensitivity to decentration errors of thereflecting surface is twice as high as that in the case of a refractingsurface, and as the number of reflections increases, decentration errorsthat are transferred while being added up increase correspondingly.Consequently, manufacturing accuracy and assembly accuracy, e.g. surfaceaccuracy and decentration accuracy, required for reflecting surfacesbecome even more strict.

SUMMARY OF THE INVENTION

[0013] In view of the above-described problems of the prior art, anobject of the present invention is to provide a high-performance andlow-cost image-forming optical system having a reduced number ofconstituent optical elements.

[0014] Another object of the present invention is to provide ahigh-performance image-forming optical system that is made compact andthin by folding an optical path using reflecting surfaces arranged tominimize the number of reflections.

[0015] To attain the above-described objects, the present inventionprovides an image-forming optical system having a positive refractingpower as a whole for forming an object image. The image-forming opticalsystem has at least one prism formed from a medium having a refractiveindex (n) larger than 1.3 (n>1.3). The prism has at least four opticalsurfaces that transmit or reflect a light beam. When image-side threesurfaces of the at least four optical surfaces are defined as a surfaceA, a surface B and a surface C in order from the image plane side of theprism, at least one of the surfaces B and C has a curved surfaceconfiguration that gives a power to a light beam. The curved surfaceconfiguration has a rotationally asymmetric surface configuration thatcorrects aberrations due to decentration. The image-forming opticalsystem leads light rays from an object to the image plane withoutforming an image in the prism and has a pupil in the prism. The surfaceA has a transmitting action by which rays internally reflected from thesurface B are allowed to exit from the prism. The surface B has areflecting action to reflect rays internally reflected from the surfaceC. The surface C has a reflecting action.

[0016] The reasons for adopting the above-described arrangement in thepresent invention, together with the function thereof, will be describedbelow in order.

[0017] The image-forming optical system according to the presentinvention, which is provided to attain the above-described objects, hasa positive refracting power as a whole for forming an object image. Theimage-forming optical system has at least one prism formed from a mediumhaving a refractive index (n) larger than 1.3 (n>1.3). The prism has atleast four optical surfaces that transmit or reflect a light beam. Theimage-forming optical system leads light rays from an object to theimage plane without forming an image in the prism and has a pupil in theprism.

[0018] A refracting optical element such as a lens is provided with apower by giving a curvature to an interface surface thereof.Accordingly, when rays are refracted at the interface surface of thelens, chromatic aberration unavoidably occurs according to chromaticdispersion characteristics of the refracting optical element.Consequently, the common practice is to add another refracting opticalelement for the purpose of correcting the chromatic aberration.

[0019] Meanwhile, a reflecting optical element such as a mirror or aprism produces no chromatic aberration in theory even when a reflectingsurface thereof is provided with a power, and need not add anotheroptical element only for the purpose of correcting chromatic aberration.Accordingly, an optical system using a reflecting optical element allowsthe number of constituent optical elements to be reduced from theviewpoint of chromatic aberration correction in comparison to an opticalsystem using a refracting optical element.

[0020] At the same time, a reflecting optical system using a reflectingoptical element allows the optical system itself to be compact in sizein comparison to a refracting optical system because the optical path isfolded in the reflecting optical system.

[0021] Reflecting surfaces require a high degree of accuracy forassembly and adjustment because they have high sensitivity todecentration errors in comparison to refracting surfaces. However, amongreflecting optical elements, prisms, in which the positionalrelationship between surfaces is fixed, only need to controldecentration as a single unit of prism and do not need high assemblyaccuracy and a large number of man-hours for adjustment as are neededfor other reflecting optical elements.

[0022] Furthermore, a prism has an entrance surface and an exit surface,which are refracting surfaces, and a reflecting surface. Therefore, thedegree of freedom for aberration correction is high in comparison to amirror, which has only a reflecting surface. In particular, if the prismreflecting surface is assigned the greater part of the desired power tothereby reduce the powers of the entrance and exit surfaces, which arerefracting surfaces, it is possible to reduce chromatic aberration to avery small quantity in comparison to refracting optical elements such aslenses while maintaining the degree of freedom for aberration correctionat a high level in comparison to mirrors. Furthermore, the inside of aprism is filled with a transparent medium having a refractive indexhigher than that of air. Therefore, it is possible to obtain a longeroptical path length than in the case of air. Accordingly, the use of aprism makes it possible to obtain an optical system that is thinner andmore compact than those formed from lenses, mirrors and so forth, whichare placed in the air.

[0023] In addition, an image-forming optical system is required toexhibit favorable image-forming performance as far as the peripheralportions of the image field, not to mention the performance required forthe center of the image field. In the case of a general coaxial opticalsystem, the sign of the ray height of extra-axial rays is inverted at astop. Accordingly, if optical elements are not in symmetry with respectto the stop, off-axis aberrations are aggravated. For this reason, thecommon practice is to place refracting surfaces at respective positionsfacing each other across the stop, thereby obtaining a satisfactorysymmetry with respect to the stop, and thus correcting off-axisaberrations.

[0024] For the reasons stated above, the present Invention adopts abasic arrangement in which the image-forming optical system has a stopin the prism and does not form an intermediate image. In addition, it isdesirable that the image-forming optical system should be approximatelytelecentric on the image side.

[0025] Next, the arrangement of an image-forming optical system that isapproximately telecentric on the image side will be described in detail.

[0026] As has been stated above, reflecting surfaces have a highdecentration error sensitivity in comparison to refracting surfaces.Therefore, it is desirable to provide an arrangement of an opticalsystem that is as independent of the high decentration error sensitivityas possible. In the case of a general coaxial optical system arranged tobe approximately telecentric on the image side, because extra-axialprincipal rays are approximately parallel to the optical axis, thepositional accuracy of the extra-axial rays is satisfactorily maintainedon the image plane even if defocusing is effected. Therefore, theimage-forming optical system according to the present invention isarranged to reflect the property of the above-described arrangement. Inparticular, to prevent the performance of an optical system using areflecting surface, which has a relatively high decentration errorsensitivity, from being deteriorated by focusing, it is desirable toadopt an arrangement in which the optical system is approximatelytelecentric on the image side, whereby the positional accuracy of extraaxial rays is maintained favorably.

[0027] Such an arrangement enables the present invention to be suitablyapplied to an image pickup optical system using an image pickup device,e.g. a CCD, in particular. Adopting the above-described arrangementminimizes the influence of the cosine fourth law. Accordingly, it isalso possible to reduce shading.

[0028] As has been stated above, adopting the basic arrangement of thepresent invention makes it possible to obtain a compact image-formingoptical system that has a smaller number of constituent optical elementsthan in the case of a refracting optical system and exhibits favorableperformance throughout the image field, from the center to the peripherythereof.

[0029] Incidentally, the prism in the present invention has animage-side part including reflecting and transmitting surfaces. That is,the image-side part of the prism includes a surface C that reflects inthe prism a light beam passing through a first transmitting surfaceplaced in a front-half part of the prism to allow a light beam to enterthe prism (in a case where another reflecting surface is provided, thesurface C reflects the light beam reflected from the reflectingsurface). The surfaces in the image-side part of the prism furtherinclude a surface B that reflects in the prism the light beam reflectedfrom the surface C, and a surface A through which the light beam exitsfrom the prism. At least one of the surfaces B and C has a curvedsurface configuration that gives a power to a light beam. The curvedsurface configuration has a rotationally asymmetric surfaceconfiguration that corrects aberrations due to decentration.

[0030] An object-side part of the prism in the present invention,exclusive of the surfaces A, B and C, has at least one reflectingsurface that reflects a light beam in the prism (the object-side partwill hereinafter be referred to as the “prism object-side part”, and thepart including the surfaces A, B and C as the “prism image-side part”).The reflecting surface has a rotationally asymmetric surfaceconfiguration that gives a power to a light beam and correctsaberrations due to decentration.

[0031] When a light ray from the object center that passes through thecenter of the stop and reaches the center of the image plane is definedas an axial principal ray, it is desirable that the at least onereflecting surface in the prism object-side part should be decenteredwith respect to the axial principal ray. If the at least one reflectingsurface in the prism object-side part is not decentered with respect tothe axial principal ray, the axial principal ray travels along the sameoptical path when incident on and reflected from the reflecting surface,and thus the axial principal ray is intercepted in the optical systemundesirably. As a result, an image is formed from only a light beamwhose central portion is shaded. Consequently, the center of the imageis unfavorably dark, or no image is formed in the center of the imagefield.

[0032] It is also possible to decenter a reflecting surface with a powerwith respect to the axial principal ray.

[0033] When a reflecting surface with a power is decentered with respectto the axial principal ray, it is desirable that at least one ofsurfaces constituting the prism used in the present invention should bea rotationally asymmetric surface. In the prism image-side part, it isparticularly preferable from the viewpoint of aberration correction thatat least one of the surfaces C and B, which are reflecting surfaces,should be a rotationally asymmetric surface. In the prism object-sidepart, it is particularly preferable from the viewpoint of aberrationcorrection that the at least one reflecting surface should be arotationally asymmetric surface.

[0034] The reasons for adopting the above-described arrangements in thepresent invention will be described below in detail.

[0035] First, a coordinate system used in the following description androtationally asymmetric surfaces will be described.

[0036] An optical axis defined by a straight line along which the axialprincipal ray travels until it intersects the first surface of theoptical system is defined as a Z-axis. An axis perpendicularlyintersecting the Z-axis in the decentration plane of each surfaceconstituting the image-forming optical system is defined as a Y-axis. Anaxis perpendicularly intersecting the optical axis and alsoperpendicularly intersecting the Y-axis is defined as an X-axis. Raytracing is forward ray-tracing in-which rays are traced from the objecttoward the image plane.

[0037] In general, a spherical lens system comprising only a sphericallens is arranged such that aberrations produced by spherical surfaces,such as spherical aberration, coma and curvature of field, are correctedwith some surfaces by canceling the aberrations with each other, therebyreducing aberrations as a whole.

[0038] On the other hand, rotationally symmetric aspherical surfaces andthe like are used to correct aberrations favorably with a minimal numberof surfaces. The reason for this is to reduce various aberrations thatwould be produced by spherical surfaces.

[0039] However, in a decentered optical system, rotationally asymmetricaberrations due to decentration cannot be corrected by a rotationallysymmetric optical system. Rotationally asymmetric aberrations due todecentration include distortion, curvature of field, and astigmatic andcomatic aberrations, which occur even on the axis.

[0040] First, rotationally asymmetric curvature of field will bedescribed. For example, when rays from an infinitely distant objectpoint are incident on a decentered concave mirror, the rays arereflected by the concave mirror to form an image. In this case, the backfocal length from that portion of the concave mirror on which the raysstrike to the image surface is a half the radius of curvature of theportion on which the rays strike in a case where the medium on theimage-side is air. Consequently, as shown in FIG. 18, an image surfacetilted with respect to the axial principal ray is formed. It isimpossible to correct such rotationally asymmetric curvature of field bya rotationally symmetric optical system.

[0041] To correct the tilted curvature of field by the concave mirror Mitself, which is the source of the curvature of field, the concavemirror M is formed from a rotationally asymmetric surface, and, in thisexample, the concave mirror M is arranged such that the curvature ismade strong (refracting power is increased) in the positive direction ofthe Y-axis, whereas the curvature is made weak (refracting power isreduced) in the negative direction of the Y-axis. By doing so, thetilted curvature of field can be corrected. It is also possible toobtain a flat image surface with a minimal number of constituentsurfaces by placing a rotationally asymmetric surface having the sameeffect as that of the above-described arrangement in the optical systemseparately from the concave mirror M.

[0042] It is preferable that the rotationally asymmetric surface shouldbe a rotationally asymmetric surface having no axis of rotationalsymmetry in the surface nor out of the surface. If the rotationallyasymmetric surface has no axis of rotational symmetry in the surface norout of the surface, the degree of freedom increases, and this isfavorable for aberration correction.

[0043] Next, rotationally asymmetric antigmatism will be described.

[0044] A decentered concave mirror M produces astigmatism even for axialrays, as shown in FIG. 19, as in the case of the above. The astigmatismcan be corrected by appropriately changing the curvatures in the X- andY-axis directions of the rotationally asymmetric surface as in the caseof the above.

[0045] Rotationally asymmetric coma will be described below.

[0046] A decentered concave mirror M produces coma even for axial rays,as shown in FIG. 20, as in the case of the above. The coma can becorrected by changing the tilt of the rotationally asymmetric surfaceaccording as the distance from the origin of the X-axis increases, andfurther appropriately changing the tilt of the surface according to thesign (positive or negative) of the Y-axis.

[0047] The image-forming optical system according to the presentinvention may also be arranged such that the above-described at leastone surface having a reflecting action is decentered with respect to theaxial principal ray and has a rotationally asymmetric surfaceconfiguration and further has a power. By adopting such an arrangement,decentration aberrations produced as the result of giving a power to thereflecting surface can be corrected by the surface itself. In addition,the power of the refracting surfaces of the prism is reduced, and thuschromatic aberration produced in the prism can be minimized.

[0048] The rotationally asymmetric surface used in the present inventionshould preferably be a plane-symmetry free-form surface having only oneplane of symmetry. Free-form surfaces used in the present invention aredefined by the following equation (a). It should be noted that theZ-axis of the defining equation is the axis of a free-form surface.$\begin{matrix}{Z = {{c\quad {r^{2}/\left\lbrack {1 + {\sqrt{\quad}\left\{ {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\}}} \right\rbrack}} + {\sum\limits_{j = 2}^{66}{C_{j}X^{m}Y^{n}}}}} & (a)\end{matrix}$

[0049] In Eq. (a), the first term is a spherical surface term, and thesecond term is a free-form surface term.

[0050] In the spherical surface term:

[0051] c: the curvature at the vertex

[0052] k: a conic constant

[0053] r={square root}{square root over ( )}(X²+Y²)

[0054] The free-form surface term is given by${{\sum\limits_{j = 2}^{66}{C_{j}X^{m}Y^{n}}} = {{C_{2}X} + {C_{3}Y} + \quad {C_{4}X^{2}} + {C_{5}X\quad Y} + {C_{6}Y^{2}} + \quad {C_{7}X^{3}} + {C_{8}X^{2}Y} + {C_{9}X\quad Y^{2}} + {C_{10}Y^{3}} + \quad {C_{11}X^{4}} + {C_{12}X^{3}Y} + {C_{13}X^{2}Y^{2}} + {C_{14}X\quad Y^{3}} + {C_{15}Y^{4}} + \quad {C_{16}X^{5}} + {C_{17}X^{4}Y} + {C_{18}X^{3}Y^{2}} + {C_{19}X^{2}Y^{3}} + \quad {C_{20}X\quad Y^{4}} + {C_{21}Y^{5}} + \quad {C_{22}X^{6}} + {C_{23}X^{5}Y} + {C_{24}X^{4}Y^{2}} + {C_{25}X^{3}Y^{3}} + \quad {C_{26}X^{2}Y^{4}} + {C_{27}X\quad Y^{5}} + {C_{28}y^{6}} + \quad {C_{29}X^{7}} + {C_{30}X^{6}Y} + {C_{31}X^{5}Y^{2}} + {C_{32}X^{4}Y^{3}} + \quad {C_{33}X^{3}Y^{4}} + {C_{34}X^{2}Y^{5}} + {C_{35}X\quad Y^{6}} + {C_{36}Y^{7}}}}\quad$

[0055] where C_(j) (j is an integer of 2 or higher) are coefficients.

[0056] In general, the above-described free-form surface does not haveplanes of symmetry in both the XZ- and YZ-planes. In the presentinvention, however, a free-form surface having only one plane ofsymmetry parallel to the YZ-plane is obtained by making all terms ofodd-numbered degrees with respect to X zero. For example, in the abovedefining equation (a), the coefficients of the terms C₂, C₅, C₇, C₉,C₁₂, C₁₄, C₁₆, C₁₈, C₂₀, C₂₃, C₂₅, C₂₇, C₂₉, C₃₁, C₃₃, C₃₅, . . . areset equal to zero. By doing so, it is possible to obtain a free-formsurface having only one plane of symmetry parallel to the YZ-plane.

[0057] A free-form surface having only one plane of symmetry parallel tothe XZ-plane is obtained by making all terms of odd-numbered degreeswith respect to Y zero. For example, in the above defining equation (a),the coefficients of the terms C₃, C₅, C₈, C₁₀, C₁₂, C₁₄, C₁₇, C₁₉, C₂₁,C₂₃, C₂₅, C₂₇, C₃₀, C₃₂, C₃₄, C₃₆, are set equal to zero. By doing so,it is possible to obtain a free-form surface having only one plane ofsymmetry parallel to the XZ-plane.

[0058] Furthermore, the direction of decentration is determined incorrespondence to either of the directions of the above-described planesof symmetry. For example, with respect to the plane of symmetry parallelto the YZ-plane, the direction of decentration off the optical system isdetermined to be the Y-axis direction. With respect to the plane ofsymmetry parallel to the XZ-plane, the direction of decentration of theoptical system is determined to be the X-axis direction. By doing so,rotationally asymmetric aberrations due to decentration can be correctedeffectively, and at the same time, productivity can be improved.

[0059] It should be noted that the above defining equation (a) is shownas merely an example, and that the feature of the present inventionresides in that rotationally asymmetric aberrations due to decentrationare corrected and, at the same time, productivity is improved by using arotationally asymmetric surface having only one plane of symmetry.Therefore, the same advantageous effect can be obtained for any otherdefining equation that expresses such a rotationally asymmetric surface.

[0060] In the present invention, the prism object-side part and theprism image-side part may be made of different materials and cementedtogether. Alternatively, the prism object-side part and the prismimage-side part may be placed adjacently to each other with a smallspacing therebetween. In either case, the advantageous effects of thepresent invention can be obtained satisfactorily.

[0061] Incidentally, it is desirable to arrange the prism optical systemsuch that the two reflecting surfaces C and B, which are placed in theimage-side part of the prism optical system, are positioned to face eachother across the prism medium, and the surface A, which has atransmitting action by which a light beam is allowed to exit from theprism, is disposed between the surfaces C and B, thereby forming aZ-shaped optical path.

[0062] As stated above, the surfaces A to C in the prism image-side partare arranged to form a Z-shaped optical path in the prism. In otherwords, the surfaces A to C are arranged such that optical paths in theprism do not intersect each other. With the above-described arrangement,directions in which the axial principal ray is incident on and reflectedfrom the surface C, respectively, are opposite to directions in whichthe axial principal ray are incident on and reflected from the surfaceB. Accordingly, it is easy to correct the optical system foraberrations, and the arrangement is favorable from the viewpoint ofdesign and aberration correcting performance.

[0063] By arranging the prism image-side part as stated above, the angleof reflection in the prism image-side part can be made gentle incomparison to a prism structure in which the entrance position to theprism image-side part and the exit surface are adjacent to each other.Accordingly, the aggravation of aberrations is reduced, and the degreeof design freedom increases.

[0064] If the prism image-side part is constructed by using tworeflecting surfaces and one transmitting surface as stated above, thedegree of freedom for aberration correction increases, and the amount ofaberration produced in the prism image-side part is favorably small. Inaddition, because the relative decentration between the two reflectingsurfaces is small, aberrations produced by the two reflecting surfacesare corrected with these reflecting surfaces by canceling theaberrations each other. Therefore, the amount of aberration produced inthe prism is favorably small. It is more desirable that the tworeflecting surfaces should have powers of different signs. By doing so,it is possible to enhance the effect of correcting each other'saberrations by the two reflecting surfaces and hence possible to obtainhigh resolution.

[0065] It is preferable to minimize the relative decentration betweenthe surfaces C and B at the respective positions where the optical axisis reflected. By doing so, it is possible to minimize the amount ofdecentration aberrations. Thus, the amount of rotationally asymmetricaberrations produced in the prism becomes small.

[0066] Accordingly, both the surfaces C and B of the prism image-sidepart may be arranged to have a rotationally asymmetric surfaceconfiguration that gives a power to a light beam and correctsaberrations due to decentration.

[0067] Furthermore, the rotationally asymmetric surface configuration ofat least one of the surfaces C and B in the prism image-side part may bearranged in the form of a plane-symmetry free-form surface having onlyone plane of symmetry.

[0068] When both the surfaces C and B of the prism image-side part haverotationally asymmetric surface configurations, the rotationallyasymmetric surface configuration of each of the two surfaces may bearranged in the form of a plane-symmetry free-form surface having onlyone plane of symmetry.

[0069] In this case, the prism image-side part may be arranged such thatthe only one plane of symmetry of the plane-symmetry free-form surfacethat forms the surface C and the only one plane of symmetry of theplane-symmetry free-form surface that forms the surface B are formed inthe same plane.

[0070] The surface A of the prism image-side part may have arotationally asymmetric surface configuration that gives a power to alight beam and corrects aberrations due to decentration. A refractingsurface having such a surface configuration is effective in correctingaberrations due to decentration.

[0071] In this case, the rotationally asymmetric surface configurationof the surface A of the prism image-side part may be arranged in theform of a plane-symmetry free-form surface having only one plane ofsymmetry.

[0072] Furthermore, a rotationally asymmetric surface placed in theprism object-side part may be arranged in the form of a plane-symmetryfree-form surface having only one plane of symmetry.

[0073] The arrangement may be such that the prism object-side part andthe prism image-side part each have at least one plane-symmetryfree-form surface having only one plane of symmetry, and the only oneplane of symmetry of the at least one plane-symmetry free-form surfacein the prism object-side part and that of the at least oneplane-symmetry free-form surface in the prism image-side part are placedin the same plane.

[0074] By using a reflecting surface having a negative refracting powerto form the prism object-side part, a wide field angle for imaging canbe obtained. This is because the negative power enables rays of widefield angle to be converged and thus it is possible to converge thelight beam when the rays are incident on a reflecting surface providedin the prism image-side part. This is favorable from the viewpoint ofaberration correction when an optical system having a relatively shortfocal length is to be constructed.

[0075] In the present invention, the effective way of enhancing thesymmetry required for the image-forming optical system and therebyfavorably correcting aberrations, including off-axis aberrations, is toplace a pupil between the prism object-side part and the prismimage-side part and to place the prism image-side part between the pupiland the image plane.

[0076] In this case, a stop can be placed on the pupil (particularly, ina case where the prism object-side part and the prism image-side partare cemented together, or they are placed adjacently to each other witha small spacing therebetween).

[0077] In the present invention, the prism object-side part, exclusiveof the surfaces A, B and C, may be arranged to have two or morereflecting surfaces with a curved-surface configuration that gives apower to a light beam.

[0078] In this case, the prism object-side part, exclusive of thesurfaces A, B and C, may be formed from two optical surfaces, i.e. anentrance surface serving as both a reflecting surface and a transmittingsurface, and a reflecting surface. In other words, the second reflectingsurface and the first transmitting surface may be formed from a singlesurface serving as both reflecting and transmitting surfaces. With thisarrangement, the first reflecting surface reflects incident rays towardthe second reflecting surface at a minimal angle of deviation, and thesecond reflecting surface bends the rays to a considerable extent.Therefore, it is possible to reduce the thickness of the prism in thedirection of the incident rays.

[0079] In a case where the prism object-side part is arranged as statedabove, it is preferable to give a negative power to the first reflectingsurface (a positive power may be locally present in the first reflectingsurface). By doing so, it is possible to lengthen the optical pathlength along an optical path between the first reflecting surface and asurface having a positive power in the prism image-side part.Consequently, the positive and negative powers of the two surfaces canbe weakened, and it becomes possible to minimize aberrations produced bythese surfaces. Thus, it is possible to maintain the required aberrationcorrecting performance and to widen the field angle most effectively.

[0080] It is preferable to place the stop on the image side of the prismobject-side part. By doing so, in a case where the first reflectingsurface has a negative power and is approximated by a spherical surface,the center of curvature of the first reflecting surface and the stopposition are approximately coincident with each other. Therefore, it ispossible to eliminate comatic aberration in theory.

[0081] In the present invention, the prism object-side part, exclusiveof the surfaces A, B and C, may comprise an entrance surface having atransmitting action by which a light beam is allowed to enter the prism,and two reflecting surfaces that give a power to a light beam.

[0082] In this case, it is particularly desirable to arrange the prismobject-side part such that the two reflecting surfaces face each otheracross the prism medium, and the entrance surface and the two reflectingsurfaces form a Z-shaped optical path.

[0083] The above-described prism configuration enables an increase inthe degree of freedom for aberration correction and produces minimalaberrations. In addition, because the relative decentration between thetwo reflecting surfaces is small, aberrations produced by the tworeflecting surfaces are corrected with these reflecting surfaces bycanceling the aberrations each other. Therefore, the amount ofaberration produced in the prism is favorably small. It is moredesirable that the two reflecting surfaces should have powers ofdifferent signs. By doing so, it is possible to enhance the effect ofcorrecting each other's aberrations by the two reflecting surfaces andhence possible to obtain high resolution.

[0084] It is even more desirable to give a negative power to the firstreflecting surface. By doing so, it is possible to lengthen the opticalpath length along an optical path between the first reflecting surfaceand a surface having a positive power in the prism image-side part.Consequently, the positive and negative powers of the two surfaces canbe weakened, and it becomes possible to minimize aberrations produced bythese surfaces. It is also preferable to place the stop on the imageside of the prism object-side part. By doing so, in a case where thefirst reflecting surface has a negative power and is approximated by aspherical surface, the center of curvature of the first reflectingsurface and the stop position are approximately coincident with eachother. Therefore, it is possible to eliminate comatic aberration intheory.

[0085] In the present invention, the prism object-side part, exclusiveof the surfaces A, B and C, may be formed from three optical surfaces,i.e. an entrance surface serving as both a reflecting surface and atransmitting surface, and two reflecting surfaces.

[0086] In this type of prism, the first transmitting surface and thesecond reflecting surface are formed from a single surface serving asboth transmitting and reflecting surfaces. The first reflecting surfacereflects incident rays toward the second reflecting surface at a minimalangle of deviation. The second reflecting surface bends rays to aconsiderable extent. The third reflecting surface bends rays at aminimal angle of deviation. Therefore, it is possible to reduce thethickness of the prism in the direction of the incident rays. Inaddition, in a case where a stop is placed between the prism object-sidepart and the prism image-side part, it is possible to lengthen theoptical path length from the stop position to the first reflectingsurface, which usually has a strong negative refracting power, in theprism. Accordingly, a thin optical system can be constructed. Moreover,the distance between the prism object-side part and the prism image-sidepart can be shortened.

[0087] By arranging the prism object-side part to have a negativerefracting power, a wide field angle for imaging can be obtained. Thisis because the negative power enables rays of wide field angle to beconverged and thus it is possible to converge the light beam when therays are incident on the second unit, which comprises the prismimage-side part. This is favorable from the viewpoint of aberrationcorrection when an optical system having a relatively short focal lengthis to be constructed.

[0088] When a prism object-side part having the above-describedarrangement is used, it is preferable for the second reflecting surfaceto effect the reflection in the prism by a totally reflecting action soas to serve as both transmitting and reflecting surfaces.

[0089] In addition, it is preferable for the first reflecting surface ofthe prism object-side part to have a reflecting surface configurationthat gives a negative power to a light beam reflected in the prism as awhole (a positive power may be locally present in the first reflectingsurface).

[0090] By virtue of the above-described arrangement, it is possible tolengthen the optical path length along an optical path between the firstreflecting surface and a surface having a positive power in the prismimage-side part. Consequently, the positive and negative powers of thetwo surfaces can be weakened, and it becomes possible to minimizeaberrations produced by these surfaces. Thus, it is possible to maintainthe required aberration correcting performance and to widen the fieldangle most effectively.

[0091] In the prism of the present invention, reflecting surfaces otherthan a totally reflecting surface are preferably formed from areflecting surface having a thin film of a metal, e.g. aluminum orsilver, formed on the surface thereof, or a reflecting surface formedfrom a dielectric multilayer film. In the case of a metal thin filmhaving reflecting action, a high reflectivity can be readily obtained.The use of a dielectric reflecting film is advantageous in a case wherea reflecting film having wavelength selectivity or minimal absorption isto be formed.

[0092] Thus, it is possible to obtain a low-cost and compactimage-forming optical system in which the prism manufacturing accuracyis favorably eased.

[0093] In the present invention, it is desirable for the image-formingoptical system to have a prism object-side part having a divergingaction on the object side of a stop and a prism image-side part having aconverging action on the image side of the stop, and also desirable forthe image-forming optical system to be approximately telecentric on theimage side.

[0094] In an image-forming optical system using a refracting opticalelement, the power distribution varies according to the use application.For example, telephoto systems having a narrow field angle generallyadopt an arrangement in which the entire system is formed as a telephototype having a positive front unit and a negative rear unit, therebymaking the overall length of the optical system shorter than the focallength. Wide-angle systems having a wide field angle generally adopt anarrangement in which the entire system is formed as a retrofocus typehaving a negative front unit and a positive rear unit, thereby makingthe back focus longer than the focal length.

[0095] In the case of an image-forming optical system using an imagepickup device, e.g. a CCD, in particular, it is necessary to place anoptical low-pass filter, an infrared cutoff filter, etc. between theimage-forming optical system and the image pickup device to remove moireand to eliminate the influence of infrared rays. Therefore, with a viewto ensuring a space for placing these optical members, it is desirableto adopt a retrofocus type arrangement for the image-forming opticalsystem.

[0096] It is important for a retrofocus type image-forming opticalsystem to be corrected for aberrations, particularly off-axisaberrations. The correction of off-axis aberrations depends largely onthe position of the stop. As has been stated above, in the case of ageneral coaxial optical system, off-axis aberrations are aggravated ifoptical elements are not in symmetry with respect to the stop. For thisreason, the common practice is to place optical elements of the samesign at respective positions facing each other across the stop, therebyobtaining a satisfactory symmetry with respect to the stop, and thuscorrecting off-axis aberrations. In the case of a retrofocus type systemhaving a negative front unit and a positive rear unit, the powerdistribution is asymmetric in the first place. Therefore, the off-axisaberration-correcting performance varies to a considerable extentaccording to the position of the stop.

[0097] Therefore, the stop is placed between the prism object-side parthaving a diverging action and the prism image-side part having aconverging action, thereby making it possible to minimize theaggravation of off-axis aberrations due to the asymmetry of the powerdistribution. If the stop is placed on the object side of the prismobject-side part having a diverging action or on the image side of theprism image-side part having a converging action, the asymmetry withrespect to the stop is enhanced and becomes difficult to correct.

[0098] In this case, the image-forming optical system may consist of aprism in which the prism object-side part of diverging action is placedon the object side of the stop, and the prism image-side part ofconverging action is placed on the image side of the stop.

[0099] In the image-forming optical systems according to the presentinvention, there is only one image-formation plane throughout thesystem. As has been stated above, the decentration error sensitivity ofa reflecting surface is higher than that of a refracting surface. In areflecting optical member arranged in the form of a single block as inthe case of a prism, surface accuracy errors and decentration errors ofeach surface are transferred while being added up. Therefore, thesmaller the number of reflecting surfaces, the more the manufacturingaccuracy required for each surface is eased. Accordingly, it isundesirable to increase the number of reflections more than is needed.For example, in an image-forming optical system in which an intermediateimage is formed and this image is relayed, the number of reflectionsincreases more than is needed, and the manufacturing accuracy requiredfor each surface becomes tight, causing the cost to increaseunfavorably.

[0100] Let us define the power of a decentered optical system and thatof a decentered optical surface. As shown in FIG. 21, when the directionof decentration of a decentered optical system S is taken in the Y-axisdirection, a light ray which is parallel to the axial principal ray ofthe decentered optical system S and which has a small height d in theYZ-plane is made to enter the decentered optical system S from theobject side thereof. The angle that is formed between that ray and theaxial principal ray exiting from the decentered optical system S as thetwo rays are projected onto the YZ-plane is denoted by δy, and δy/d isdefined as the power Py in the Y-axis direction of the decenteredoptical system S. Similarly, a light ray which is parallel to the axialprincipal ray of the decentered optical system S and which has a smallheight d in the X-axis direction, which is perpendicular to theYZ-plane, is made to enter the decentered optical system S from theobject side thereof. The angle that is formed between that ray and theaxial principal ray exiting from the decentered optical system S as thetwo rays are projected onto a plane perpendicularly intersecting theYZ-plane and containing the axial principal ray is denoted by δx, andδx/d is defined as the power Px in the X-axis direction of thedecentered optical system S. The power Pyn in the Y-axis direction andpower Pxn in the X-axis direction of a decentered optical surface nconstituting the decentered optical system S are defined in the same wayas the above.

[0101] Furthermore, the reciprocals of the above-described powers aredefined as the focal length Fy in the, Y-axis direction of thedecentered optical system S, the focal length Fx in the X-axis directionof the decentered optical system S, the focal length Fyn in the Y-axisdirection of the decentered optical surface n, and the focal length Fxnin the X-axis direction of the decentered optical surface n,respectively.

[0102] When the powers in the X- and Y-axis directions of the surface Bhaving a reflecting action are denoted by Pxb and Pyb, respectively, andthe powers in the X- and Y-axis directions of the prism are denoted byPx and Py, respectively, it is preferable to satisfy the followingcondition:

0<Pxb/Px<5  (1)

[0103] The condition (1) limits the power of the surface B having areflecting action in the prism image-side part. The surface B needs tohave a relatively strong power in the whole optical system. The surfaceB is characterized in that because it has a relatively small amount ofdecentration with respect to rays, even if the surface B has a strongpower, it produces a relatively small amount of decentrationaberrations.

[0104] If Pxb/Px is not larger than the lower limit of the condition(1), i.e. 0, the surface B has no power. Consequently, another surfaceneeds to have a strong power, and the amount of decentration aberrationsproduced by this surface becomes unfavorably large. If Pxb/Px is notsmaller than the upper limit of the condition (1), i.e. 5, the power ofthe surface B becomes excessively strong, and the amount of decentrationaberrations produced by the surface B becomes unfavorably large.

[0105] It is even more desirable to satisfy the following condition:

0<Pxb/Px<2  (1-1)

[0106] It is still more desirable to satisfy the following condition:

0<Pxb/Px<1  (1-2)

[0107] It is also preferable to satisfy the following condition:

0<Pyb/Py<5  (2)

[0108] The meaning of the condition (2) is the same as that of thecondition (1). Therefore, a description thereof is omitted.

[0109] It is even more desirable to satisfy the following condition:

0<Pyb/Py<2  (2-1)

[0110] It is still more desirable to satisfy the following condition:

0<Pyb/Py<1  (2-2)

[0111] When the powers in the X- and Y-axis directions of the surface Chaving a reflecting action are denoted by Pxc and Pyc, respectively, andthe powers in the X- and Y-axis directions of the prism are denoted byPx and Py, respectively, it is preferable to satisfy the followingcondition:

−5<Pxc/Px<5  (3)

[0112] The condition (3) limits the power of the surface C having areflecting action in the prism image-side part. The surface C needs tohave a relatively strong power in the whole optical system. The surfaceC is characterized in that because it has a relatively small amount ofdecentration with respect to rays, even if the surface C has a strongpower, it produces a relatively small amount of decentrationaberrations.

[0113] If Pxc/Px is not larger than the lower limit of the condition(3), i.e. −5, the negative power of the surface C becomes excessivelystrong. Consequently, another surface needs to have a strong positivepower, and the amount of decentration aberrations produced by thissurface becomes unfavorably large. If Pxc/Px is not smaller than theupper limit of the condition (3), i.e. 5, the power of the surface Cbecomes excessively strong, and the amount of decentration aberrationsproduced by the surface C becomes unfavorably large.

[0114] It is even more desirable to satisfy the following condition:

−2<Pxc/Px<2  (3-1)

[0115] It is still more desirable to satisfy the following condition:

−1<Pxc/Px<1  (3-2)

[0116] It is also preferable to satisfy the following condition:

−5<Pyc/Py<5  (4)

[0117] The meaning of the condition (4) is the same as that of thecondition (3). Therefore, a description thereof is omitted.

[0118] It is even more desirable to satisfy the following condition:

−2<Pyc/Py<2  (4-1)

[0119] It is still more desirable to satisfy the following condition:

−1<Pyc/Py<1  (4-2)

[0120] Next, when the incident angles of the axial principal ray on thesurfaces B and C are denoted by αb and αc, respectively, it ispreferable to satisfy the following condition:

5°<αb<45°  (5)

[0121] The condition (5) relates to the power of the surface B. If αb isnot larger than the lower limit of the condition (5), i.e. 5°, raysincident on the surface B are undesirably intercepted by the surface C.Accordingly, it becomes impossible to construct the desired opticalsystem. If αb is not smaller than the upper limit of the condition (5),i.e. 45°, the amount of decentration becomes excessively large.Consequently, decentration aberrations produced by the surface B becomeexcessively large and hence impossible to correct by another surface.

[0122] It is even more desirable to satisfy the following condition:

10°<αb<40°  (5-1)

[0123] It is still more desirable to satisfy the following conditions:

20°<αb<30  (5-2)

[0124] It is also preferable to satisfy the following condition:

5°<αc<45°  (6)

[0125] The condition (6) relates to the power of the surface C. If αc isnot larger than the lower limit of the condition (6), i.e. 5°, raysincident on the surface C are undesirably intercepted by the surface B.Accordingly, it becomes impossible to construct the desired opticalsystem. If αc is not smaller than the upper limit of the condition (6),i.e. 45°, the amount of decentration becomes excessively large.Consequently, decentration aberrations produced by the surface C becomeexcessively large and hence impossible to correct by another surface.

[0126] It is even more desirable to satisfy the following condition:

10°<αc<40°  (6-1)

[0127] It is still more desirable to satisfy the following conditions:

20°<αc<30°  (6-2)

[0128] Next, when the ratio of αc to αb, i.e. αc/αb, is denoted by αbc,it is preferable to satisfy the following condition:

0.6<abc<1.4  (7)

[0129] The condition (7) is a condition for a portion of the prismimage-side part that forms a Z-shaped optical path. The feature of theZ-shaped optical path resides in that the optical path length from apoint on the surface C at which the axial principal ray is reflected bythe surface C to a point on the surface B at which the axial principalray is reflected by the surface B is relatively uniform independently ofthe field angle. Thus, the resultant total power of the two reflectingsurfaces C and B is uniform independently of the field angle,advantageously.

[0130] If αbc is not larger than the lower limit of the condition (7),i.e. 0.6, or not smaller than the upper limit, i.e. 1.4, the Z-shapedoptical path is unfavorably distorted, and decentration aberrationsproduced by the surfaces B and C become unfavorably large and impossibleto correct by another surface because the surfaces B and C are assignedthe greater part of the overall power of the optical system.

[0131] It is even more desirable to satisfy the following condition:

0.8<αbc<1.2  (7-1)

[0132] It is still more desirable to satisfy the following condition:

0.9<αbc<1.1  (7-2)

[0133] Next, in a case where the prism object-side part has at least tworeflecting surfaces, when the powers in the X- and Y-axis directions ofthe first reflecting surface are denoted by Px1 and Py1, respectively,and the powers in the X- and Y-axis directions of the prism are denotedby Px and Py, respectively, it is preferable to satisfy the followingcondition:

−5<Px1/Px<0  (8)

[0134] If Px1/Px is not larger than the lower limit of the condition(8), i.e. −5, the negative power of the first reflecting surface becomesexcessively strong. Consequently, decentration aberrations, particularlyimage distortion due to decentration, produced by this surface becomelarge and hence difficult to correct by another surface. If Px1/Px isnot smaller than the upper limit of the condition (8), i.e. 0, aretrofocus type optical system cannot be realized, and it becomesdifficult to ensure a wide field angle for observation.

[0135] To ensure a horizontal half field angle of 15° or more, inparticular, it is even more desirable to satisfy the followingcondition:

−3<Px1/Px<−0.3  (8-1)

[0136] It is also preferable to satisfy the following condition:

−4<Py1/Py<0  (9)

[0137] If Py1/Py is not larger than the lower limit of the condition(9), i.e. −4, the negative power of the first reflecting surface becomesexcessively strong. Consequently, decentration aberrations, particularlyimage distortion due to decentration, produced by this surface becomelarge and hence difficult to correct by another surface. If Py1/Py isnot smaller than the upper limit of the condition (9), i.e. 0, aretrofocus type optical system cannot be realized, and it becomesdifficult to ensure a wide field angle for observation.

[0138] To ensure a horizontal half field angle of 15° or more, inparticular, it is even more desirable to satisfy the followingcondition:

−2<Py1/Py<−0.1  (9-1)

[0139] When the powers in the X- and Y-axis directions of the secondreflecting surface are denoted by Px2 and Py2, respectively, and thepowers in the X- and Y-axis directions of the prism are denoted by Pxand Py, respectively, it is preferable to satisfy the followingcondition:

−2<Px2/Px<4  (10)

[0140] The condition (10) is a condition for the second reflectingsurface. The second reflecting surface reflects rays at a large angle tolead them to the image plane. Accordingly, the angle at which rays areincident on the second reflecting surface is large. If Px2/Px is notlarger than the lower limit of the condition (10), i.e. −2, or notsmaller than the upper limit, i.e. 4, the second reflecting surface hasan excessively strong power. Consequently, decentration aberrationsproduced by this surface become excessively large and hence impossibleto correct by another surface. Because the second reflecting surface isrelatively close to the stop position, decentration aberrations,particularly coma due to decentration, produced by this surface becomelarge and hence difficult to correct by another surface.

[0141] It is even more desirable to satisfy the following condition:

−1<Px2/Px<2  (10-1)

[0142] It is still more desirable to satisfy the following condition:

−0.4<Px2/Px<1  (10-2)

[0143] It is also preferable to satisfy the following condition:

−2<Py2/Py<2  (11)

[0144] The condition (11) is also a condition for the second reflectingsurface. The second reflecting surface reflects rays at a large angle tolead them to the image plane. Accordingly, the angle at which rays areincident on the second reflecting surface is large. If Py2/Py is notlarger than the lower limit of the condition (11), i.e. −2, or notsmaller than the upper limit, i.e. 2, the second reflecting surface hasan excessively strong power. Consequently, decentration aberrationsproduced by this surface become excessively large and hence impossibleto correct by another surface. Because the second reflecting surface isrelatively close to the stop position, decentration aberrations,particularly coma due to decentration, produced by this surface becomelarge and hence difficult to correct by another surface.

[0145] It is even more desirable to satisfy the following condition:

−1<Py2/Py<0.8  (11-1)

[0146] It is still more desirable to satisfy the following condition:

−0.8<Py2/Py<0.4  (11-2)

[0147] In the image-forming optical system according to the presentinvention, focusing of the image-forming optical system can be effectedby moving all the constituent elements or moving the prism. However, itis also possible to effect focusing by moving the image-formation planein the direction of the axial principal ray exiting from the surfaceclosest to the image side. By doing so, it is possible to preventdisplacement of the axial principal ray on the entrance side due tofocusing even if the direction in which the axial principal ray from theobject enters the optical system is not coincident with the direction ofthe axial principal ray exiting from the surface closest to the imageside owing to the decentration of the image-forming optical system. Itis also possible to effect focusing by moving a plurality ofwedge-shaped prisms, which are formed by dividing a plane-parallelplate, in a direction perpendicular to the Z-axis. In this case also,focusing can be performed independently of the decentration of theimage-forming optical system.

[0148] In the present invention, temperature compensation can be made byforming the prism object-side part and the prism image-side part usingdifferent materials. By providing the prism object-side part and theprism image-side part with powers of different signs, it is possible toprevent the focal shift due to changes in temperature, which is aproblem arising when a plastic material is used to form a prism.

[0149] In a case where the two prism parts of the present invention arecemented together, it is desirable that each of the two prism partsshould have a positioning portion for setting a relative position on asurface having no optical action. In a case where two prism parts eachhaving a reflecting surface with a power are cemented together as in thepresent invention, in particular, relative displacement of each prismpart causes the performance to be deteriorated. Therefore, in thepresent invention, a positioning portion for setting a relative positionis provided on each surface of each prism part that has no opticalaction, thereby ensuring the required positional accuracy. Thus, thedesired performance can be ensured. In particular, if the two prismparts are integrated into one unit by using the positioning portions andcoupling members, it becomes unnecessary to perform assembly adjustment.Accordingly, the cost can be further reduced.

[0150] Furthermore, the optical path can be folded in a directiondifferent from the decentration direction of the image-forming opticalsystem according to the present invention by placing a reflectingoptical member, e.g. a mirror, on the object side of the entrancesurface of the image-forming optical system. By doing so, the degree offreedom for layout of the image-forming optical system furtherincreases, and the overall size of the image-forming optical apparatuscan be further reduced.

[0151] In the present invention, the image-forming optical system can beformed from a prism alone. By doing so, the number of components isreduced, and the cost is lowered. Furthermore, two prisms may beintegrated into one prism with a stop put therebetween. By doing so, thecost can be further reduced.

[0152] In the present invention, the image-forming optical system mayinclude another lens (positive or negative lens) as a constituentelement in addition to the prism at either or each of the object andimage sides of the prism.

[0153] The image-forming optical system according to the presentinvention may be a fast, single focal length lens system. Alternatively,the image-forming optical system may be arranged in the form of a zoomlens system (variable-magnification image-forming optical system) bycombining it with a single or plurality of refracting optical systemsthat may be provided on the object or image side of the prism.

[0154] In the present invention, the refracting and reflecting surfacesof the image-forming optical system may be formed from sphericalsurfaces or rotationally symmetric aspherical surfaces.

[0155] In a case where the above-described image-forming optical systemaccording to the present invention is placed in an image pickup part ofan image pickup apparatus, or in a case where the image pickup apparatusis a photographic apparatus having a camera mechanism it is possible toadopt an arrangement in which a prism member is placed closest to theobject side among optical elements having an optical action, and theentrance surface of the prism member is decentered with respect to theoptical axis, and further a cover member is placed on the object side ofthe prism member at right angles to the optical axis. The arrangementmay also be such that the prism member has on the object side thereof anentrance surface decentered with respect to the optical axis, and acover lens having a power is placed on the object side of the entrancesurface of the prism member in coaxial relation to the optical axis soas to face the entrance surface across an air spacing.

[0156] If a prism member is placed closest to the object side and adecentered entrance surface is provided on the front side of aphotographic apparatus as stated above, the obliquely tilted entrancesurface is seen from the subject, and it gives the illusion that thephotographic center of the apparatus is deviated from the subject whenthe entrance surface is seen from the subject side. Therefore, a covermember or a cover lens is placed at right angles to the optical axis,thereby preventing the subject from feeling incongruous when seeing theentrance surface, and allowing the subject to be photographed with thesame feeling as in the case of general photographic apparatus.

[0157] A finder optical system can be formed by using any of theabove-described image-forming optical systems according to the presentinvention as a finder objective optical system and adding animage-inverting optical system for erecting an object image formed bythe finder objective optical system and an ocular optical system.

[0158] In addition, it is possible to construct a camera apparatus byusing the finder optical system and an objective optical system forphotography provided in parallel to the finder optical system.

[0159] In addition, an image pickup optical system can be constructed byusing any of the foregoing image-forming optical systems according tothe present invention and an image pickup device placed in an imageplane formed by the image-forming optical system.

[0160] In addition, a camera apparatus can be constructed by using anyof the foregoing image-forming optical systems according to the presentinvention as an objective optical system for photography, and a finderoptical system placed in an optical path separate from an optical pathof the objective optical system for photography or in an optical pathsplit from the optical path of the objective optical system forphotography.

[0161] In addition, an electronic camera apparatus can be constructed byusing any of the foregoing image-forming optical systems according tothe present invention, an image pickup device placed in an image planeformed by the image-forming optical system, a recording medium forrecording image information received by the image pickup device, and animage display device that receives image information from the recordingmedium or the image pickup device to form an image for observation.

[0162] In addition, an endoscope system can be constructed by using anobservation system having any of the foregoing image-forming opticalsystems according to the present invention and an image transmittingmember for transmitting an image formed by the image-forming opticalsystem along a longitudinal axis, and an illumination system having anilluminating light source and an illuminating light transmitting memberfor transmitting illuminating light from the illuminating light sourcealong the longitudinal axis.

[0163] Still other objects and advantages of the invention will in partbe obvious and will in part be apparent from the specification.

[0164] The invention accordingly comprises the features of construction,combinations of elements, and arrangement of parts which will beexemplified in the construction hereinafter set forth, and the scope ofthe invention will be indicated in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0165]FIG. 1 is a sectional view of an image-forming optical systemaccording to Example 1 of the present invention.

[0166]FIG. 2 is a sectional view of an image-forming optical systemaccording to Example 2 of the present invention.

[0167]FIG. 3 is a sectional view of an image-forming optical systemaccording to Example 3 of the present invention.

[0168]FIG. 4 is a sectional view of an image-forming optical systemaccording to Example 4 of the present invention.

[0169]FIG. 5 is a sectional view of an image-forming optical systemaccording to Example 5 the present invention.

[0170]FIG. 6 is a sectional view of an image-forming optical systemaccording to Example 6 of the present invention.

[0171]FIG. 7 is a sectional view of an image-forming optical systemaccording to Example 10 of the present invention.

[0172]FIG. 8 is a sectional view of an image-forming optical systemaccording to Example 13 of the present invention.

[0173]FIG. 9 is a sectional view of an image-forming optical systemaccording to Example 15 of the present invention.

[0174]FIG. 10 is an aberrational diagram showing lateral aberrations inthe image-forming optical system according to Example 1.

[0175]FIG. 11 is a perspective view showing the external appearance ofan electronic camera to which an image-forming optical system accordingto the present invention is applied, as viewed from the front sidethereof.

[0176]FIG. 12 is a perspective view of the electronic camera shown inFIG. 11, as viewed from the rear side thereof.

[0177]FIG. 13 is a sectional view showing the arrangement of theelectronic camera in FIG. 11.

[0178]FIG. 14 is a conceptual view of another electronic camera to whichan image-forming optical system according to the present invention isapplied.

[0179]FIG. 15 is a conceptual view of a video endoscope system to whichan image-forming optical system according to the present invention isapplied.

[0180]FIG. 16 is a conceptual view showing an arrangement in which aprism optical system according to the present invention is applied to aprojection optical system of a presentation system.

[0181]FIG. 17 is a diagram showing a desirable arrangement for animage-forming optical system according to the present invention when itis placed in front of an image pickup device.

[0182]FIG. 18 is a conceptual view for describing curvature of fieldproduced by a decentered reflecting surface.

[0183]FIG. 19 is a conceptual view for describing astigmatism producedby a decentered reflecting surface.

[0184]FIG. 20 is a conceptual view for describing coma produced by adecentered reflecting surface.

[0185]FIG. 21 is a diagram for describing the definition of the power ofa decentered optical system and the power of a decentered opticalsurface.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0186] Examples 1 to 15 of the image-forming optical system according tothe present invention will be described below. It should be noted thatconstituent parameters of each example will be shown later.

[0187] In each example, as shown in FIG. 1, an axial principal ray 1 isdefined by a ray emanating from the center of an object and passingthrough the center of a stop 2 to reach the center of an image plane 3.A hypothetic plane is taken in a plane extending through theintersection between the axial principal ray 1 and an entrance surface(first surface) 11 of a prism 10 at right angles to the axial principalray 1 entering the entrance surface 11. Another hypothetic plane istaken in a plane extending through the intersection between the axialprincipal ray 1 and an exit surface (surface A) A of the prism 10 atright angles to the axial principal ray 1 exiting from the exit surfaceA. Further, a reference plane is taken in a stop (pupil) plane 2. Theintersection of each hypothetic plane and the associated optical surfaceand the intersection between the axial principal ray 1 and the stopplane 2 are each defined as the origin for decentered optical surfacespresent between the optical surface and the stop plane 2 or thehypothetic plane subsequent thereto (the image plane in the case of thefinal hypothetic plane). In the case of the hypothetic plane determinedwith respect to the intersection of the entrance surface and in the caseof the stop plane 2, a Z-axis is taken in the direction of the axialprincipal ray 1 incident thereon. In the case of the hypothetic planedetermined with respect to the intersection of the exit surface, aZ-axis is taken in the direction of the axial principal rays exitingfrom the exit surface. With respect to the first hypothetic planepassing through the intersection between the axial principal ray 1 andthe entrance surface (first surface) 11 of the prism 10, a positivedirection of the Z-axis is taken in the direction of travel of the axialprincipal ray 1. With respect to the stop plane 2 and the hypotheticplane regarding the exit surface, a positive direction of the Z-axis istaken in the direction of travel of the axial principal ray 1 in a casewhere there are an even number of reflections in the optical path fromthe first hypothetic plane to the stop plane 2 or from the stop plane 2to the subsequent hypothetic plane. In a case where the number ofreflections is an odd number, a positive direction of the Z-axis istaken in an opposite direction to the direction of travel of the axialprincipal ray 1. A plane containing the Z-axis and the center of theimage plane 3 is defined as a YZ-plane. An axis extending through theorigin at right angles to the YZ-plane is defined as an X-axis. Thedirection in which the X-axis extends from the obverse side toward thereverse side of the plane of the figure is defined as a positivedirection of the X-axis. An axis that constitutes a right-handedorthogonal coordinate system in combination with the X- and Z-axes isdefined as a Y-axis. FIG. 1 shows the hypothetic planes and a coordinatesystem concerning the first hypothetic plane determined with respect tothe intersection of the entrance surface 11. Illustration of thehypothetic planes and the coordinate system is omitted in FIG. 2 and thesubsequent figures.

[0188] In Example 1 to 15, the decentration of each surface is made inthe YZ-plane, and the one and only plane of symmetry of eachrotationally asymmetric free-form surface is the YZ-plane.

[0189] Regarding decentered surfaces, each surface is givendisplacements in the X-, Y- and Z-axis directions (X, Y and Z,respectively) of the vertex position of the surface from the origin ofthe associated coordinate system, and tilt angles (degrees) of thecenter axis of the surface [the Z-axis of the above equation (a) inregard to free-form surfaces] with respect to the X-, Y- and Z-axes (α,β and γ, respectively). In this case, positive a and 0 meancounterclockwise rotation relative to the positive directions of thecorresponding axes, and positive γ means clockwise rotation relative tothe positive direction of the Z-axis.

[0190] Among optical surfaces constituting the optical system in eachexample, a specific surface (including a hypothetic plane) and a surfacesubsequent thereto are given a surface separation when these surfacesform a coaxial optical system. In addition, the refractive index andAbbe's number of each medium are given according to the conventionalmethod. It should be noted that the sign of the surface separation isshown to be a positive value in a case where there are an even number ofreflections in the optical path from the first hypothetic plane to thereference optical surface (including a hypothetic plane), whereas in acase where the number of reflections is an odd number, the sign of thesurface separation is shown-to be a negative value. However, thedistances in the direction of travel of the axial principal ray 1 areall positive values.

[0191] The configuration of each free-form surface used in the presentinvention is defined by the above equation (a). The Z-axis of thedefining equation is the axis of the free-form surface.

[0192] In the constituent parameters (shown later), those termsconcerning free-form surfaces for which no data is shown are zero. Therefractive index is expressed by the refractive index for the spectrald-line (wavelength: 587.56 nanometers). Lengths are given inmillimeters.

[0193] Free-form surfaces may also be defined by Zernike polynomials.That is, the configuration of a free-form surface may be defined by thefollowing equation (b). The Z-axis of the defining equation (b) is theaxis of Zernike polynomial. A rotationally asymmetric surface is definedby polar coordinates of the height of the Z-axis with respect to theXY-plane. In the equation (b), A is the distance from the Z-axis in theXY-plane, and R is the azimuth angle about the Z-axis, which isexpressed by the angle of rotation measured from the Z-axis.$\begin{matrix}{{{x = {R \times {\cos (A)}}}{y = {R \times {\sin (A)}}}Z = {D_{2} + {D_{3}R\quad {\cos (A)}} + {D_{4}R\quad {\sin (A)}} + \quad {D_{5}R^{2}\quad {\cos \left( {2A} \right)}} + {D_{6}\left( {R^{2} - 1} \right)} + {D_{7}R^{2}\quad {\sin \left( {2A} \right)}} + \quad {D_{8}R^{3}\quad {\cos \left( {3A} \right)}} + {{D_{9}\left( {{3R^{3}} - {2R}} \right)}{\cos (A)}} + \quad {{D_{10}\left( {{3R^{3}} - {2R}} \right)}{\sin (A)}} + {D_{11}R^{3}{\sin \left( {3A} \right)}} + \quad {D_{12}R^{4}\quad {\cos \left( {4A} \right)}} + {{D_{13}\left( {{4R^{4}} - {3R^{2}}} \right)}{\cos \left( {2A} \right)}} + \quad {D_{14}\left( {{6R^{4}} - {6R^{2}} + 1} \right)} + {{D_{15}\left( {{4R^{4}} - {3R^{2}}} \right)}{\sin \left( {2A} \right)}} + \quad {D_{16}R^{4}{\sin \left( {4A} \right)}} + \quad {D_{17}R^{5}\quad {\cos \left( {5A} \right)}} + {{D_{18}\left( {{5R^{5}} - {4R^{3}}} \right)}{\cos \left( {3A} \right)}} + \quad {{D_{19}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}{\cos (A)}} + \quad {{D_{20}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}{\sin (A)}} + \quad {{D_{21}\left( {{5R^{5}} - {4R^{3}}} \right)}{\sin \left( {3A} \right)}} + {D_{22}R^{5}{\sin \left( {5A} \right)}} + \quad {D_{23}R^{6}\quad {\cos \left( {6A} \right)}} + {{D_{24}\left( {{6R^{6}} - {5R^{4}}} \right)}{\cos \left( {4A} \right)}} + \quad {{D_{25}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}{\cos \left( {2A} \right)}} + \quad {D_{26}\left( {{20R^{6}} - {30R^{4}} + {12R^{2}} - 1} \right)} + \quad {{D_{27}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}{\sin \left( {2A} \right)}} + \quad {{D_{28}\left( {{6R^{6}} - {5R^{4}}} \right)}{\sin \left( {4A} \right)}} + {D_{29}R^{6}{\sin \left( {6A} \right)}}}}\quad} & (b)\end{matrix}$

[0194] In the above equation, to design an optical system symmetric withrespect to the X-axis direction, D₄, D₅, D₆, D₁₀, D₁₁, D₁₂, D₁₃, D₁₄,D₂₀, D₂₁, D₂₂ . . . should be used.

[0195] Other examples of surfaces usable in the present invention areexpressed by the following defining equation (c):

Z=ΣΣC _(nm) XY

[0196] Assuming that k=7 (polynomial of degree 7), for example, afree-form surface is expressed by an expanded form of the above equationas follows: $\begin{matrix}{Z = {C_{2} + {C_{3}y} + {C_{4}{x}} + \quad {C_{5}y^{2}} + {C_{6}y{x}} + {C_{7}x^{2}} + \quad {C_{8}y^{3}} + {C_{9}y^{2}{x}} + {C_{10}y\quad x^{2}} + {C_{11}{x^{3}}} + \quad {C_{12}y^{4}} + {C_{13}y^{3}{x}} + {C_{14}y^{2}x^{2}} + {C_{15}y{x^{3}}} + {C_{16}x^{4}} + \quad {C_{17}y^{5}} + {C_{18}y^{4}{x}} + {C_{19}y^{3}x^{2}} + {C_{20}y^{2}{x^{3}}} + \quad {C_{21}y\quad x^{4}} + {C_{22}{x^{5}}} + \quad {C_{23}y^{6}} + {C_{24}y^{5}{x}} + {C_{25}y^{4}x^{2}} + {C_{26}y^{3}{x^{3}}} + \quad {C_{27}y^{2}x^{4}} + {C_{28}y{x^{5}}} + {C_{29}x^{6}} + \quad {C_{30}y^{7}} + {C_{31}y^{6}{x}} + {C_{32}y^{5}x^{2}} + {C_{33}y^{4}{x^{3}}} + \quad {C_{34}y^{3}x^{4}} + {C_{35}y^{2}{x^{5}}} + {C_{36}y\quad x^{6}} + {C_{37}{x^{7}}}}} & (c)\end{matrix}$

[0197] Although in the examples of the present invention the surfaceconfiguration is expressed by a free-form surface using the aboveequation (a), it should be noted that the same advantageous effect canbe obtained by using the above equation (b) or (c).

[0198] In all Examples 1 to 15, photographic field angles are asfollows: The horizontal half field angle is 26.3°, and the vertical halffield angle is 20.3°. The size of the image pickup device is 3.2×2.4millimeters. F-number is 2.8. The focal length is equivalent to about3.27 millimeters. The image-forming optical system according to eachexample can be applied to other sizes, as a matter of course. Thepresent invention includes not only an image pickup optical system usingthe image-forming optical system according to the present invention butalso an image pickup apparatus incorporating the optical system.

EXAMPLES 1 AND 7

[0199]FIG. 1 is a sectional view of Example 1 taken along the YZ-planecontaining the axial principal ray. The sectional view of Example 7 issimilar to FIG. 1. Therefore, illustration of Example 7 is omitted.Constituent parameters of these examples will be shown later. In theconstituent parameters, free-form surfaces are denoted by “FFS”, andhypothetic planes by “HRP” (Hypothetic Reference Plane). The same shallapply to the other examples.

[0200] Examples 1 and 7 each have, in order in which light passes fromthe object side, an object-side part of a prism 10, a stop 2, animage-side part of the prism 10, and an image plane (image-formationplane) 3. The object-side part of the prism 10 comprises an entrancesurface 11 as a first surface, a first reflecting surface 12, and asecond reflecting surface 13 formed from the first surface 11, whichalso serves as the entrance surface 11. The image-side part of the prism10 comprises a surface C as a third reflecting surface, a surface B as afourth reflecting surface, and a surface A as an exit surface. Rays froman object enter through the entrance surface 11 and are reflectedsuccessively by the first reflecting surface 12 and the secondreflecting surface 13. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.In the object-side part of the prism 10, the entrance surface 11 and thesecond reflecting surface 13 are the identical optical surface havingboth transmitting and reflecting actions.

[0201] In the constituent parameters (shown later), the displacements ofeach of the surface Nos. 2 to 5 are expressed by the amounts ofdisplacement from the hypothetic plane 1 of surface No. 1. Thedisplacements of each of the surface Nos. 6 to 9 are expressed by theamounts of displacement from the stop plane 2 of surface No. 5. Theimage plane is expressed by only the surface separation along the axialprincipal ray from the hypothetic plane 2 of surface No. 9.

EXAMPLES 2 AND 8

[0202]FIG. 2 is a sectional view of Example 2 taken along the YZ-planecontaining the axial principal ray. The sectional view of Example 8 issimilar to FIG. 2. Therefore, illustration of Example 8 is omitted.Constituent parameters of these examples will be shown later.

[0203] Examples 2 and 8 each have, in order in which light passes fromthe object side, an object-side part of a prism 10, a stop 2, animage-side part of the prism 10, and an image plane (image-formationplane) 3. The object-side part of the prism 10 comprises an entrancesurface 11 as a first surface, a first reflecting surface 12, and asecond reflecting surface 13 formed from the first surface 11, whichalso serves as the entrance surface 11. The image-side part of the prism10 comprises a surface C as a third reflecting surface, a surface B as afourth reflecting surface, and a surface A as an exit surface. Rays froman object enter through the entrance surface 11 and are reflectedsuccessively by the first reflecting surface 12 and the secondreflecting surface 13. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.In the object-side part of the prism 10, the entrance surface 11 and thesecond reflecting surface 13 are the identical optical surface havingboth transmitting and reflecting actions. It should be noted thatExamples 2 and 8 differ from Examples 1 and 7 in that the direction inwhich the rays are reflected from the surface C in Examples 2 and 8 isopposite to that in Examples 1 and 7.

[0204] In the constituent parameters (shown later), the displacements ofeach of the surface Nos. 2 to 5 are expressed by the amounts ofdisplacement from the hypothetic plane 1 of surface No. 1. Thedisplacements of each of the surface Nos. 6 to 9 are expressed by theamounts of displacement from the stop plane 2 of surface No. 5. Theimage plane is expressed by only the surface separation along the axialprincipal ray from the hypothetic plane 2 of surface No. 9.

EXAMPLES 3 AND 9

[0205]FIG. 3 is a sectional view of Example 3 taken along the Y-Z-planecontaining the axial principal ray. The sectional view of Example 9 issimilar to FIG. 3. Therefore, illustration of Example 9 is omitted.Constituent parameters of these examples will be shown later.

[0206] Examples 3 and 9 each have, in order in which light passes fromthe object side, an object-side part of a prism 10, a stop 2, animage-side part of the prism 10, and an image plane (image-formationplane) 3. The object-side part of the prism 10 comprises an entrancesurface 11 as a first surface, a first reflecting surface 12, and asecond reflecting surface 13. The image-side part of the prism 10comprises a surface C as a third reflecting surface, a surface B as afourth reflecting surface, and a surface A as an exit surface. Rays froman object enter through the entrance surface 11 and are reflectedsuccessively by the first reflecting surface 12 and the secondreflecting surface 13. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.

[0207] In the constituent parameters (shown later), the displacements ofeach of the surface Nos. 2 to 5 are expressed by the amounts ofdisplacement from the hypothetic plane 1 of surface No. 1. Thedisplacements of each of the surface Nos. 6 to 9 are expressed by theamounts of displacement from the stop plane 2 of surface No. 5. Theimage plane is expressed by only the surface separation along the axialprincipal ray from the hypothetic plane 2 of surface No. No. 9.

EXAMPLES 4, 10 AND 13

[0208]FIGS. 4, 7 and 8 are sectional views of Examples 4, 10 and 13,respectively, taken along the YZ-plane containing the axial principalray. Constituent parameters of these examples will be shown later.

[0209] Examples 4, 10 and 13 each have, in order in which light passesfrom the object side, an object-side part of a prism 10, a stop 2, animage-side part of the prism 10, and an image plane (image-formationplane) 3. The object-side part of the prism 10 comprises an entrancesurface 11 as a first surface, a first reflecting surface 12, and asecond reflecting surface 13. The image-side part of the prism 10comprises a surface C as a third reflecting surface, a surface B as afourth reflecting surface, and a surface A as an exit surface. Rays froman object enter through the entrance surface 11 and are reflectedsuccessively by the first reflecting surface 12 and the secondreflecting surface 13. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.It should be noted that Examples 4, 10 and 13 differ from Examples 3 and9 in that the direction in which the rays are reflected from the surfaceC in Examples 4, 10 and 13 is opposite to that in Examples 3 and 9.

[0210] In the constituent parameters (shown later), the displacements ofeach of the surface Nos. 2 to 5 are expressed by the amounts ofdisplacement from the hypothetic plane 1 of surface No. 1. Thedisplacements of each of the surface Nos. 6 to 9 are expressed by theamounts of displacement from the stop plane 2 of surface No. 5. Theimage plane is expressed by only the surface separation along the axialprincipal ray from the hypothetic plane 2 of surface No. 9.

EXAMPLES 5, 11 AND 14

[0211]FIG. 5 is a sectional view of Example 5 taken along the YZ-planecontaining the axial principal ray. The sectional views of Examples 11and 14 are similar to FIG. 5. Therefore, illustration of Examples 11 and14 is omitted. Constituent parameters of these examples will be shownlater.

[0212] Examples 5, 11 and 14 each have, in order in which light passesfrom the object side, an object-side part of a prism 10, a stop 2, animage-side part of the prism 10, and an image plane (image-formationplane) 3. The object-side part of the prism 10 comprises an entrancesurface 11 as a first surface, a first reflecting surface 12, a secondreflecting surface 13 formed from the first surface 11, which alsoserves as the entrance surface 11, and a third reflecting surface 14.The image-side part of the prism 10 comprises a surface C as a fourthreflecting surface, a surface B as a fifth reflecting surface, and asurface A as an exit surface. Rays from an object enter through theentrance surface 11 and are reflected successively by the firstreflecting surface 12, the second reflecting surface 13 and the thirdreflecting surface 14. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.In the object-side., part of the prism 10, the entrance surface 11 andthe second reflecting surface 13 are the identical optical surfacehaving both transmitting and reflecting actions.

[0213] In the constituent parameters (shown later), the displacements ofeach of the surface Nos. 2 to 6 are expressed by the amounts ofdisplacement from the hypothetic plane 1 of surface No. 1. Thedisplacements of each of the surface Nos. 7 to 10 are expressed by theamounts of displacement from the stop plane 2 of surface No. 6. Theimage plane is expressed by only the surface separation along the axialprincipal ray from the hypothetic plane 2 of surface No. 10.

EXAMPLES 6, 12 AND 15

[0214]FIGS. 6 and 9 are sectional views of Examples 6 and 15,respectively, taken along the YZ-plane containing the axial principalray. The sectional view of Example 12 is similar to these figures.Therefore, illustration of Example 12 is omitted. Constituent parametersof these examples will be shown later.

[0215] Examples 6, 12 and 15 each have, in order in which light passesfrom the object side, an object-side part of a prism 10, a stop 2, animage-side part of the prism 10, and an image plane (image-formationplane) 3. The object-15 side part of the prism 10 comprises an entrancesurface 11 as a first surface, a first reflecting surface 12, a secondreflecting surface 13 formed from the first surface 11, which alsoserves as the entrance surface 11, and a third reflecting surface 14.The image-side part of the prism 10 comprises a surface C as a fourthreflecting surface, a surface B as a fifth reflecting surface, and asurface A as an exit surface. Rays from an object enter through theentrance surface 11 and are reflected successively by the firstreflecting surface 12, the second reflecting surface 13 and the thirdreflecting surface 14. Then, the rays pass through the stop (pupil) 2and are reflected successively by the surface C and the surface B andthen pass through the surface A to form an image on the image plane 3.In the object-side part of the prism 10, the entrance surface 11 and thesecond reflecting surface 13 are the identical optical surface havingboth transmitting and reflecting actions. It should be noted thatExamples 6, 12 and 15 differ from Examples 5, 11 and 14 in that thedirection in which the rays are reflected from the surface C in Examples6, 12 and 15 is opposite to that in Examples 5, 11 and 14.

[0216] In the constituent parameters (shown later), the displacements ofeach of the surface Nos. 2 to 6 are expressed by the amounts ofdisplacement from the hypothetic plane 1 of surface No. 1. Thedisplacements of each of the surface Nos. 7 to 10 are expressed by theamounts of displacement from the stop plane 2 of surface No. 6. Theimage plane is expressed by only the surface separation along the axialprincipal ray from the hypothetic plane 2 of surface No. 10.

[0217] Constituent parameters in the foregoing Examples 1 to 15 areshown below. In the tables below, “FFS” denotes a free-form surface, and“HRP” denotes a hypothetic plane.

EXAMPLE 1

[0218] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle over (3)} (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 9 ∞ (HRP2) 2.09 (7) Image ∞ planeFFS{circle over (1)} C₄ 1.0213 × 10⁻³ C₆ 2.6453 × 10⁻³ FFS{circle over(2)} C₄ 3.6831 × 10⁻² C₆ 3.1506 × 10⁻² FFS{circle over (3)} C₄ −1.9619 ×10⁻²  C₆ −1.4927 × 10⁻²  FFS{circle over (4)} C₄ 1.4377 × 10⁻² C₆ 1.6300× 10⁻² FFS{circle over (5)} C₄ 2.3346 × 10⁻² C₆ 7.0472 × 10⁻²Displacement and tilt(1) X 0.00 Y 2.03 Z −0.55 α 14.76 β 0.00 γ 0.00Displacement and tilt(2) X 0.00 Y 0.13 Z 1.46 α −19.14 β 0.00 γ 0.00Displacement and tilt(3) X 0.00 Y 3.85 Z 0.01 α 72.95 β 0.00 γ 0.00Displacement and tilt(4) X 0.00 Y 0.00 Z 8.65 α −16.44 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y 5.14 Z 0.70 α −15.34 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y 5.44 Z 8.55 α 20.59 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y 5.44 Z 8.55 α −7.51 β 0.00 γ 0.00

EXAMPLE 2

[0219] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle over (3)} (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 9 ∞ (HRP2) 1.90 (7) Image ∞ planeFFS{circle over (1)} C₄ 2.0637 × 10⁻² C₆ −3.3192 × 10⁻³  FFS{circle over(2)} C₄ 3.0378 × 10 ⁻² C₆ 1.1176 × 10 ⁻² FFS{circle over (3)} C₄ −5.5702× 10⁻³  C₆ −1.7581 × 10⁻²  FFS{circle over (4)} C₄ 2.8728 × 10⁻² C₆1.8483 × 10 ⁻² FFS{circle over (5)} C₄ −1.3836 × 10⁻⁴  C₆ 9.0601 × 10 ⁻²Displacement and tilt(1) X 0.00 Y 5.52 Z 0.61 α −5.19 β 0.00 γ 0.00Displacement and tilt(2) X 0.00 Y −0.17 Z 4.03 α −30.69 β 0.00 γ 0.00Displacement and tilt(3) X 0.00 Y 8.01 Z 2.80 α 48.57 β 0.00 γ 0.00Displacement and tilt(4) X 0.00 Y 0.00 Z 6.01 α 19.78 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y −4.37 Z 0.72 α 18.78 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y −4.56 Z 6.08 α −15.78 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y −4.56 Z 6.08 α 5.04 β 0.00 γ 0.00

EXAMPLE 3

[0220] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle over (4)} (5) 1.4924 57.6 7 FFS{circle over (5)} (6) 1.492457.6 8 FFS{circle over (6)} (7) 9 ∞ (HRP2) 2.81 (8) Image ∞ planeFFS{circle over (1)} C₄ 4.7101 × 10⁻³ C₆ −1.2652 × 10⁻²  FFS{circle over(2)} C₄ 1.5845 × 10⁻² C₆ 1.5053 × 10⁻² FFS{circle over (3)} C₄ −1.3680 ×10⁻²  C₆ 8.6156 × 10⁻³ FFS{circle over (4)} C₄ −2.5267 × 10⁻²  C₆−5.4885 × 10⁻³  FFS{circle over (5)} C₄ 1.9895 × 10⁻² C₆ 2.3998 × 10⁻²FFS{circle over (6)} C₄ 3.8200 × 10⁻³ C₆ 4.6234 × 10⁻² Displacement andtilt(1) X 0.00 Y 0.00 Z 0.00 α 26.39 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y 0.33 Z 2.08 α −25.10 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 4.84 Z −0.60 α −18.42 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 5.76 Z 1.63 α 22.43 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 0.00 Z 3.70 α −25.27 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y 4.41 Z 0.07 α −27.00 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y 4.17 Z 4.08 α 18.86 β 0.00 γ 0.00 Displacement andtilt(8) X 0.00 Y 4.17 Z 4.08 α −15.66 β 0.00 γ 0.00

EXAMPLE 4

[0221] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle over (4)} (5) 1.4924 57.6 7 FFS{circle over (5)} (6) 1.492457.6 8 FFS{circle over (6)} (7) 9 ∞ (HRP2) 2.62 (8) Image ∞ planeFFS{circle over (1)} C₄ 2.8191 × 10⁻² C₆ 2.4229 × 10⁻² FFS{circle over(2)} C₄ 2.9443 × 10⁻² C₆ 1.5005 × 10⁻² FFS{circle over (3)} C₄ 2.2659 ×10⁻² C₆ 5.5456 × 10⁻³ FFS{circle over (4)} C₄ −1.7340 × 10⁻³  C₆ −7.3468× 10⁻³  FFS{circle over (5)} C₄ 3.2881 × 10⁻³ C₆ 2.3399 × 10⁻²FFS{circle over (6)} C₄ −2.2289 × 10⁻²  C₆ 6.9150 × 10⁻³ Displacementand tilt(1) X 0.00 Y 0.00 Z 0.00 α −19.38 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y −0.94 Z 8.19 α −33.31 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 7.82 Z 3.15 α −20.32 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y 8.93 Z 6.31 α 19.46 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 0.00 Z 3.35 α 29.52 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y −3.73 Z 1.11 α 26.00 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y −4.02 Z 3.45 α −24.90 β 0.00 γ 0.00 Displacement andtilt(8) X 0.00 Y −4.02 Z 3.45 α 2.36 β 0.00 γ 0.00

EXAMPLE 5

[0222] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 FFS{circle over (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 1.4924 57.6 9 FFS{circle over (6)} (7)10 ∞ (HRP2) −2. 53 (8) Image ∞ plane FFS{circle over (1)} C₄ 3.2161 ×10⁻² C₆ 1.1131 × 10⁻² FFS{circle over (2)} C₄ 2.9358 × 10⁻² C₆ 2.4124 ×10⁻² FFS{circle over (3)} C₄ 4.5395 × 10⁻² C₆ 1.0726 × 10⁻² FFS{circleover (4)} C₄ 2.7116 × 10⁻² C₆ 2.2939 × 10⁻² FFS{circle over (5)} C₄−1.3722 × 10⁻²  C₆ −7.9613 × 10⁻³  FFS{circle over (6)} C₄ 1.0985 × 10⁻²C₆ −1.6177 × 10⁻³  Displacement and tilt(1) X 0.00 Y 2.45 Z −0.60 α12.05 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.20 Z 2.19 α−16.98 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 8.59 Z 2.51 α11.60 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 11.10 Z −0.47 α−39.95 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 0.00 Z −4.97 α20.63 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y 3.86 Z −0.57 α16.79 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y 4.45 Z −4.95 α−23.53 β 0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y 4.45 Z −4.95 α0.54 β 0.00 γ 0.00

EXAMPLE 6

[0223] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 FFS{circle over (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 1.4924 57.6 9 FFS{circle over (6)} (7)10 ∞ (HRP2) −2.48 (8) Image ∞ plane FFS{circle over (1)} C₄ 2.6501 ×10⁻² C₆ −4.4906 × 10⁻³  FFS{circle over (2)} C₄ 3.2328 × 10⁻² C₆ 6.2858× 10⁻³ FFS{circle over (3)} C₄ 4.6833 × 10⁻³ C₆ −9.1587 × 10⁻³ FFS{circle over (4)} C₄ 9.3385 × 10⁻³ C₆ 1.0377 × 10⁻² FFS{circle over(5)} C₄ −3.0642 × 10⁻²  C₆ −1.8737 × 10⁻²  FFS{circle over (6)} C₄−7.5684 × 10⁻³  C₆ −1.9285 × 10⁻²  Displacement and tilt(1) X 0.00 Y5.66 Z 1.47 α −13.02 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y−0.39 Z 4.18 α −35.62 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y9.18 Z 5.69 α 10.58 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y10.30 Z 2.39 α −18.65 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y0.00 Z −3.97 α −21.85 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y−3.21 Z −0.61 α −19.95 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y−3.44 Z −4.00 α 19.52 β 0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y−3.44 Z −4.00 α −4.34 β 0.00 γ 0.00

EXAMPLE 7

[0224] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle over (3)} (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 9 ∞ (HRP2) 2.09 (7) Image ∞ planeFFS{circle over (1)} C₄ 1.8037 × 10⁻³ C₆ 5.9979 × 10⁻⁴ C₈ −4.2189 × 10⁻³C₁₀ −6.1622 × 10⁻⁴  FFS{circle over (2)} C₄ 2.9790 × 10⁻² C₆ 1.5970 ×10⁻² C₈ −6.6963 × 10⁻³ C₁₀ −2.2231 × 10⁻³  FFS{circle over (3)} C₄−2.4370 × 10⁻²  C₆ −1.1867 × 10⁻²  C₈ −2.7358 × 10⁻⁴ C₁₀ 1.0226 × 10⁻⁴FFS{circle over (4)} C₄ 3.9939 × 10⁻³ C₆ 1.8938 × 10−2 C₈ −3.1418 × 10⁻⁵C₁₀ 1.5226 × 10⁻⁴ FFS{circle over (5)} C₄ −3.9043 × 10⁻²  C₆ 3.8003 ×10⁻² C₈  2.5494 × 10⁻² Displacement and tilt(1) X 0.00 Y 1.61 Z −0.85 α27.52 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.32 Z 1.90 α−7.70 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 8.75 Z 0.40 α80.10 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 0.00 Z 6.64 α−18.90 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 4.62 Z 0.69 α−17.71 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y 4.85 Z 6.40 α27.82 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y 4.85 Z 6.40 α−12.06 β 0.00 γ 0.00

EXAMPLE 8

[0225] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 ∞ (Stop) (3) 1.4924 57.6 6FFS{circle over (3)} (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 9 ∞ (HRP2) 1.12 (7) Image ∞ planeFFS{circle over (1)} C₄ 2.2304 × 10⁻² C₆ 6.7813 × 10⁻⁴ C₈ 1.1812 × 10⁻³C₁₀ −3.3872 × 10⁻⁴  FFS{circle over (2)} C₄ 3.1480 × 10⁻² C₆ 1.2842 ×10⁻² C₈ 2.0530 × 10⁻³ C₁₀ −2.3129 × 10⁻⁴  FFS{circle over (3)} C₄−8.7252 × 10⁻³  C₆ −1.4882 × 10⁻²  C₈ 1.2779 × 10⁻³ C₁₀ −3.1090 × 10⁻⁴ FFS{circle over (4)} C₄ 2.8592 × 10⁻² C₆ 2.1296 × 10⁻² C₈ −1.4838 ×10⁻⁵  C₁₀ −4.9595 × 10⁻⁴  FFS{circle over (5)} C₄ 9.2639 × 10⁻² C₆−1.7009 × 10⁻²  C₈ −1.9762 × 10⁻²  Displacement and tilt(1) X 0.00 Y7.05 Z 0.64 α −6.42 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y−0.08 Z 4.76 α −30.48 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y8.88 Z 2.34 α 47.14 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 0.00Z 5.52 α 20.19 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y −4.13 Z0.67 α 18.77 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y −4.40 Z6.02 α −7.46 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −4.40 Z6.02 α −0.55 β 0.00 γ 0.00

EXAMPLE 9

[0226] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle over (4)} (5) 1.4924 57.6 7 FFS{circle over (5)} (6) 1.492457.6 8 FFS{circle over (6)} (7) 9 ∞ (HRP2) 2.97 (8) Image ∞ planeFFS{circle over (1)} C₄ −8.2788 × 10⁻³  C₆ 3.0759 × 10⁻² C₈ 2.5136 ×10⁻³ FFS{circle over (2)} C₄ 1.5271 × 10⁻² C₆ 6.5200 × 10⁻³ C₈ 2.0313 ×10⁻⁴ C₁₀ 3.8831 × 10⁻⁴ FFS{circle over (3)} C₄ −7.1872 × 10⁻³  C₆ 2.8529× 10⁻² C₈ 1.0926 × 10⁻³ C₁₀ −1.1652 × 10⁻⁴  FFS{circle over (4)} C₄−2.5205 × 10⁻²  C₆ −1.8722 × 10⁻²  C₈ −9.9093 × 10⁻⁴  C₁₀ −3.7485 ×10⁻⁴  FFS{circle over (5)} C₄ 1.2857 × 10⁻² C₆ 2.1262 × 10⁻² C₈ −7.0303× 10⁻⁴  C₁₀ −4.4194 × 10⁻⁴  FFS{circle over (6)} C₄ 1.0973 × 10⁻³ C₆3.2543 × 10⁻² C₈ 1.1063 × 10⁻² Displacement and tilt(1) X 0.00 Y 0.00 Z0.00 α 33.59 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 1.10 Z 5.23α −20.07 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 7.63 Z 0.12 α−16.48 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 8.56 Z 2.81 α19.02 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 0.00 Z 4.81 α−24.08 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y 4.62 Z 0.67 α−21.89 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y 4.93 Z 4.68 α28.01 β 0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y 4.93 Z 4.68 α−8.73 β 0.00 γ 0.00

EXAMPLE 10

[0227] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle over (4)} (5) 1.4924 57.6 7 FFS{circle over (5)} (6) 1.492457.6 8 FFS{circle over (6)} (7) 9 ∞ (HRP2) 2.05 (8) Image ∞ planeFFS{circle over (1)} C₄ 1.4974 × 10⁻² C₆ 3.0277 × 10⁻² C₈ 2.0441 × 10⁻³FFS{circle over (2)} C₄ 3.0398 × 10⁻² C₆ 1.2528 × 10⁻² C₈ 1.4776 × 10⁻³C₁₀ 3.2717 × 10⁻⁴ FFS{circle over (3)} C₄ 2.7429 × 10⁻² C₆ 4.8497 × 10⁻³C₈ 1.5116 × 10⁻³ C₁₀ 3.1159 × 10⁻⁴ FFS{circle over (4)} C₄ 1.4459 × 10⁻²C₆ −5.2512 × 10⁻³  C₈ 2.6999 × 10⁻³ C₁₀ 1.3731 × 10⁻³ FFS{circle over(5)} C₄ 4.5648 × 10⁻² C₆ 2.9908 × 10⁻² C₈ −1.8723 × 10⁻⁴ C₁₀ 2.9008 ×10⁻⁵ FFS{circle over (6)} C₄ 9.6063 × 10⁻² C₆ 3.8186 × 10⁻² C₈ −1.4149 ×10⁻³ Displacement and tilt(1) X 0.00 Y 0.00 Z 0.00 α 0.51 β 0.00 γ 0.00Displacement and tilt(2) X 0.00 Y 0.01 Z 3.84 α −40.64 β 0.00 γ 0.00Displacement and tilt(3) X 0.00 Y 12.88 Z 1.91 α −39.14 β 0.00 γ 0.00Displacement and tilt(4) X 0.00 Y 13.07 Z 5.39 α 3.17 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y 0.00 Z 3.67 α 27.48 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y −3.89 Z 0.94 α 26.31 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y −4.03 Z 4.30 α −2.44 β 0.00 γ 0.00Displacement and tilt(8) X 0.00 Y −4.03 Z 4.30 α −2.29 β 0.00 γ 0.00

EXAMPLE 11

[0228] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 FFS{circle over (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 1.4924 57.6 9 FFS{circle over (6)} (7)10 ∞ (HRP2) 2.21 (8) Image ∞ plane FFS{circle over (1)} C₄ 3.5962 × 10⁻²C₆ 5.4714 × 10⁻³ C₈ 1.9678 × 10⁻⁴ C₁₀ −6.0817 × 10⁻⁵  FFS{circle over(2)} C₄ 1.9131 × 10⁻² C₆ 1.2344 × 10⁻² C₈ 1.5524 × 10⁻⁴ C₁₀ −4.1196 ×10⁻⁵  FFS{circle over (3)} C₄ 1.0316 × 10⁻¹ C₆ 7.4898 × 10⁻³ C₈ 1.3280 ×10⁻³ C₁₀ −2.1775 × 10⁻⁵  FFS{circle over (4)} C₄ 3.4735 × 10⁻² C₆ 1.2912× 10⁻² C₈ 1.9341 × 10⁻³ C₁₀ 8.8579 × 10⁻⁴ FFS{circle over (5)} C₄−1.9926 × 10⁻²  C₆ −2.9281 × 10⁻²  C₈ 1.0094 × 10⁻³ C₁₀ 3.2240 × 10⁻⁵FFS{circle over (6)} C₄ 9.5170 × 10⁻³ C₆ −1.0035 × 10⁻¹  C₈ −2.3170 ×10⁻³  C₁₀ 3.2652 × 10⁻³ Displacement and tilt(1) X 0.00 Y 3.96 Z −0.29 α2.88 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.09 Z 2.68 α−25.34 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 10.65 Z 3.85 α5.78 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 13.10 Z 1.54 α−46.71 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 0.00 Z −4.20 α24.79 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y 4.03 Z −0.77 α22.24 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y 4.36 Z −4.45 α−10.22 β 0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y 4.36 Z −4.45 α−2.56 β 0.00 γ 0.00

EXAMPLE 12

[0229] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 FFS{circle over (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 1.4924 57.6 9 FFS{circle over (6)} (7)10 ∞ (HRP2) −2.88 (8) Image ∞ plane FFS{circle over (1)} C₄  2.0263 ×10⁻² C₆ 1.2117 × 10⁻² C₈  1.0420 × 10⁻⁴ C₁₀  2.5388 × 10⁻⁵ FFS{circleover (2)} C₄  3.0101 × 10⁻² C₆ 1.5268 × 10⁻² C₈  1.0629 × 10⁻³ C₁₀−3.5613 × 10⁻⁴ FFS{circle over (3)} C₄ −6.4453 × 10⁻³ C₆ 1.2679 × 10⁻²C₈ −9.5533 × 10⁻⁴ C₁₀ −2.3927 × 10⁻⁵ FFS{circle over (4)} C₄ −4.5819 ×10⁻³ C₆ −3.6206 × 10⁻⁴  C₈ −4.6337 × 10⁻³ C₁₀ −1.8811 × 10⁻³ FFS{circleover (5)} C₄ −4.2725 × 10⁻² C₆ −4.1080 × 10⁻²  C₈ −1.3108 × 10⁻³ C₁₀ 1.3700 × 10⁻⁴ FFS{circle over (6)} C₄ −4.0288 × 10⁻² C₆ −1.0079 × 10⁻¹ C₈  7.3427 × 10⁻³ Displacement and tilt(1) X 0.00 Y 8.49 Z 2.91 α −24.96β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y −0.38 Z 4.92 α −40.79 β0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 10.84 Z 7.46 α −5.87 β0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 12.95 Z 4.86 α −39.03 β0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 0.00 Z −2.93 α −27.97 β0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y −3.17 Z −0.79 α −26.57 β0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −3.28 Z −3.11 α 13.08 β0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y −3.28 Z −3.11 α −2.34 β0.00 γ 0.00

EXAMPLE 13

[0230] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (3)} (3) 1.4924 57.6 5 ∞ (Stop) (4) 1.4924 57.6 6FFS{circle over (4)} (5) 1.4924 57.6 7 FFS{circle over (5)} (6) 1.492457.6 8 FFS{circle over (6)} (7) 9 ∞ (HRP2) 2.19 (8) Image ∞ planeFFS{circle over (1)} C₄  2.1612 × 10⁻² C₆ 2.2441 × 10⁻² C₈  3. 3142 ×10⁻³ C₁₃ −1.5450 × 10⁻⁶ FFS{circle over (2)} C₄  5.5239 × 10⁻² C₆ 1.7639× 10⁻² C₈  2.1076 × 10⁻³ C₁₀ −1.8254 × 10⁻⁶ C₁₁ −3.3814 × 10⁻⁴  C₁₃−7.3502 × 10⁻⁵ C₁₅ −6.3238 × 10⁻⁵ FFS{circle over (3)} C₄  3.2587 × 10⁻²C₆ 9.7605 × 10⁻³ C₈  7.0727 × 10⁻⁴ C₁₀ −6.4128 × 10⁻⁵ C₁₁ 3.0837 × 10⁻⁵C₁₃ −9.0003 × 10⁻⁵ C₁₅ −6.1904 × 10⁻⁵ FFS{circle over (4)} C₄  1.7641 ×10⁻² C₆ −3.1484 × 10⁻³  C₈  1.4327 × 10⁻³ C₁₀  7.8898 × 10⁻⁴ C₁₁ −5.7451× 10⁻⁴  C₁₃ −8.3755 × 10⁻⁴ C₁₅ −2.4142 × 10⁻⁴ FFS{circle over (5)} C₄ 5.2642 × 10⁻² C₆ 3.6812 × 10⁻² C₈ −1.1918 × 10⁻³ C₁₀ −9.1978 × 10⁻⁴ C₁₁−3.6615 × 10⁻⁴  C₁₃ −6.0092 × 10⁻⁴ C₁₅ −1.8114 × 10⁻⁴ FFS{circle over(6)} C₄  1.1608 × 10⁻¹ C₆ 1.5090 × 10⁻¹ C₈ −4.5791 × 10⁻³ C₁₃ −4.1698 ×10⁻³ Displacement and tilt(1) X 0.00 Y 0.00 Z 0.00 α −1.76 β 0.00 γ 0.00Displacement and tilt(2) X 0.00 Y −0.04 Z 3.97 α −41.02 β 0.00 γ 0.00Displacement and tilt(3) X 0.00 Y 10.28 Z 2.41 α −40.73 β 0.00 γ 0.00Displacement and tilt(4) X 0.00 Y 10.28 Z 9.89 α 0.00 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y 0.00 Z 3.35 α 29.33 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y −3.58 Z 1.17 α 28.72 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y −3.64 Z 3.78 α −3.74 β 0.00 γ 0.00Displacement and tilt(8) X 0.00 Y −3.64 Z 3.78 α 0.00 β 0.00 γ 0.00

EXAMPLE 14

[0231] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 FFS{circle over (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 1.4924 57.6 9 FFS{circle over (6)} (7)10 ∞ (HRP2) −2.33 (8) Image ∞ plane FFS{circle over (1)} C₄  4.0827 ×10⁻² C₆ 5.9635 × 10⁻³ C₈ 1.1461 × 10⁻⁴ C₁₀ −2.1507 × 10⁻⁴ C₁₁ 5.1208 ×10⁻⁵ C₁₃ 3.2010 × 10⁻⁵ C₁₅ −6.7233 × 10⁻⁶ FFS{circle over (2)} C₄ 2.7721 × 10⁻² C₆ 1.4635 × 10⁻² C₈ 2.4781 × 10⁻⁴ C₁₀ −2.2813 × 10⁻⁴ C₁₁−2.5928 × 10⁻⁵  C₁₃ −7.5774 × 10⁻⁵  C₁₅ −2 0345 × 10⁻⁵ FFS{circle over(3)} C₄  1.1023 × 10⁻¹ C₆ 9.4811 × 10⁻³ C₈ 3.2039 × 10⁻³ C₁₀ −1.5865 ×10⁻⁴ C₁₁ 2.8756 × 10⁻³ C₁₃ 5.8910 × 10⁻⁴ C₁₅  3.1494 × 10⁻⁵ FFS{circleover (4)} C₄  3.4559 × 10⁻² C₆ 1.5109 × 10⁻² C₈ 1.9022 × 10⁻³ C₁₀ 7.2864 × 10⁻⁴ C₁₁ −2.8143 × 10⁻⁵  C₁₃ 2.4265 × 10⁻⁵ C₁₅ −3.0473 × 10⁻⁵FFS{circle over (5)} C₄ −2.1578 × 10⁻² C₆ −2.9940 × 10⁻²  C₈ 8.7484 ×10−⁴ C₁₀ −1.7100 × 10⁻⁴ C₁₁ 1.9611 × 10⁻⁶ C₁₃ −4.7297 × 10⁻⁵  C₁₅−8.0783 × 10⁻⁵ FFS{circle over (6)} C₄  3.9290 × 10⁻³ C₆ −1.4942 × 10⁻¹ C₈ −9.2481 × 10⁻³  C₁₀ −4.6761 × 10⁻³ C₁₁ −1.5588 × 10⁻³  C₁₃ −3.3748 ×10⁻³  C₁₅ −1.2423 × 10⁻² Displacement and tilt(1) X 0.00 Y 3.76 Z −0.37α 4.15 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.12 Z 2.90 α−22.85 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 10.18 Z 3.90 α5.11 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 12.22 Z 1.94 α−46.17 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 0.00 Z −4.39 α24.21 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y 4.03 Z −0.82 α23.85 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y 4.08 Z −4.66 α−7.45 β 0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y 4.08 Z −4.66 α2.64 β 0.00 γ 0.00

EXAMPLE 15

[0232] Surface Radius of Surface Displacement Refractive Abbe's No.curvature separation and tilt index No. Object ∞ ∞ plane 1 ∞ (HRP1) 2FFS{circle over (1)} (1) 1.4924 57.6 3 FFS{circle over (2)} (2) 1.492457.6 4 FFS{circle over (1)} (1) 1.4924 57.6 5 FFS{circle over (3)} (3)1.4924 57.6 6 ∞ (Stop) (4) 1.4924 57.6 7 FFS{circle over (4)} (5) 1.492457.6 8 FFS{circle over (5)} (6) 1.4924 57.6 9 FFS{circle over (6)} (7)10 ∞ (HRP2) −3.07 (8) Image ∞ plane FFS{circle over (1)} C₄ 2.3309 ×10⁻² C₆ 9.9932 × 10⁻³ C₈  2.4136 × 10⁻⁴ C₁₀ 1.1090 × 10⁻⁴ C₁₁ 1.4334 ×10⁻⁴ C₁₃ −6.0188 × 10⁻⁵ C₁₅ −3.9163 × 10⁻⁶  FFS{circle over (2)} C₄4.1433 × 10⁻² C₆ 1.6695 × 10⁻² C₈  1.5395 × 10⁻³ C₁₀ −1.1536 × 10⁻⁴  C₁₁2.0588 × 10⁻⁴ C₁₃ −l.5721 × 10⁻⁴ C₁₅ −6.3666 × 10⁻⁵  FFS{circle over(3)} C₄ −9.6739 × 10⁻³  C₆ 6.2716 × 10⁻³ C₈ −2.9572 × 10⁻⁵ C₁₀ 4.3548 ×10⁻⁴ C₁₁ 3.2750 × 10⁻⁴ C₁₃  1.5172 × 10⁻⁵ C₁₅ 1.0324 × 10⁻⁴ FFS{circleover (4)} C₄ 2.0722 × 10⁻³ C₆ 6.4918 × 10⁻³ C₈ −4.2437 × 10⁻³ C₁₀−1.9251 × 10⁻³  C₁₁ 6.3713 × 10⁻⁴ C₁₃ −2.0539 × 10⁻⁶ C₁₅ 3.2793 × 10⁻⁵FFS{circle over (5)} C₄ −4.1173 × 10⁻²  C₆ −3.7458 × 10⁻²  C₈ −4.0580 ×10⁻³ C₁₀ 2.3875 × 10⁻⁴ C₁₁ 3.7267 × 10⁻⁴ C₁₃  8.2371 × 10⁻⁴ C₁₅ −2.9197× 10⁻⁵  FFS{circle over (6)} C₄ −8.6169 × 10⁻²  C₆ −1.5015 × 10⁻¹  C₈−3.2168 × 10⁻² C₁₁ −4.0638 × 10⁻³  C₁₃ −6.9267 × 10⁻³  C₁₅ −8.1027 ×10⁻³ Displacement and tilt(1) X 0.00 Y 8.37 Z 2.43 α −20.50 β 0.00 γ0.00 Displacement and tilt(2) X 0.00 Y −0.39 Z 5.35 α −37.89 β 0.00 γ0.00 Displacement and tilt(3) X 0.00 Y 11.32 Z 7.40 α 1.33 β 0.00 γ 0.00Displacement and tilt(4) X 0.00 Y 13.09 Z 4.04 α −27.92 β 0.00 γ 0.00Displacement and tilt(5) X 0.00 Y 0.00 Z −2.14 α −35.59 β 0.00 γ 0.00Displacement and tilt(6) X 0.00 Y −3.39 Z −0.99 α −35.28 β 0.00 γ 0.00Displacement and tilt(7) X 0.00 Y −3.41 Z −2.53 α 9.75 β 0.00 γ 0.00Displacement and tilt(8) X 0.00 Y −3.41 Z −2.53 α −3.93 β 0.00 γ 0.00

[0233]FIG. 10 is an aberrational diagram showing lateral aberrations inthe above-described Example 1. In the diagram showing lateralaberrations, the numerals in the parentheses denote [horizontal(X-direction) field angle, vertical (Y-direction) field angle], andlateral aberrations at the field angles are shown.

[0234] It should be noted that the values of the conditions (1) to (11)in the above-described Examples 1 to 15 are as follows: Cond. Ex. 1 Ex.2 Ex. 3 Ex. 4 Ex. 5 Ex. 6 Ex. 7 Ex. 8 (1) 0.32 0.63 0.45 0.75 0.30 0.650.08 0.61 (2) 0.38 0.42 0.58 0.53 0.18 0.42 0.39 0.44 (3) 0.44 0.12 0.570.04 −0.60 0.20 0.51 0.19 (4) 0.35 0.40 0.13 0.17 0.51 0.23 0.24 0.31(5) 16.84 21.59 22.97 33.64 23.33 24.47 19.42 22.35 (6) 16.61 19.7625.26 29.62 20.56 22.05 18.96 20.25 (7) 0.99 0.92 1.10 0.88 0.88 0.900.98 0.91 (8) −0.83 −0.66 −0.35 −0.67 −0.65 −0.69 −0.62 0.68 (9) −0.73−0.25 −0.37 −0.34 −0.53 −0.14 −0.33 −0.26 (10) 0.02 0.45 −0.31 0.51 0.710.56 0.04 0.48 (11) 0.06 −0.07 0.21 0.13 0.25 −0.10 0.01 0.01 Cond. Ex.9 Ex. 10 Ex. 11 Ex. 12 Ex. 13 Ex. 14 Ex. 15 (1) 0.28 0.97 0.45 0.92 1.020.42 0.81 (2) 0.44 0.60 0.59 0.81 0.73 0.58 0.72 (3) 0.54 −0.31 0.78−0.10 −0.34 0.67 0.04 (4) 0.38 0.11 0.26 −0.01 0.06 0.29 0.12 (5) 25.6229.35 26.54 30.06 30.83 23.65 36.89 (6) 24.38 27.56 24.87 27.85 29.4824.35 35.66 (7) 0.95 0.94 0.94 0.93 0.96 1.03 0.97 (8) −0.33 −0.64 −0.43−0.65 −1.08 −0.54 −0.81 (9) −0.13 −0.25 −0.25 −0.30 −0.35 −0.29 −0.32(10) −0.16 0.58 0.81 0.43 0.63 0.80 0.46 (11) −0.59 0.10 0.11 0.24 0.190.12 0.19

[0235] In the above-described examples, the object-side part of theprism 10, which constitute the image-forming optical system according tothe present invention, uses a prism of the type in which there are twoor three internal reflections as stated in Examples 1 to 15. It should,however, be noted that prisms usable as the object-side part of theprism 10 in the image-forming optical system according to the presentinvention are not necessarily limited to the described type. Examples ofprisms usable in the present invention include a prism in which there isone internal reflection, and prisms arranged in the same way as inExamples 5, 6, 11, 12, 14 and 15 except that the first reflectingsurface 12 and the third reflecting surface 14 are formed from theidentical surface. It is also possible to use prisms arranged in thesame way as in Examples 5, 6, 11, 12, 14 and 15 except that the secondreflecting surface 13 is formed from a surface different from theentrance surface 11.

[0236] Incidentally, the above-described image-forming optical systemaccording to the present invention can be used in photographicapparatus, particularly in cameras, in which an object image formed bythe image-forming optical system is received with an image pickupdevice, such as a CCD or a silver halide film, to take a photograph ofthe object. It is also possible to use the image-forming optical systemas an objective optical system of an observation apparatus in which anobject image is viewed through an ocular lens, particularly a finderunit of a camera. The image-forming optical system according to thepresent invention is also usable as an image pickup optical system foroptical apparatus using a small-sized image pickup device, e.g.endoscopes. Embodiments in which the present invention is applied tosuch apparatuses will be described below.

[0237] FIGS. 11 to 13 are conceptual views showing an arrangement inwhich the image-forming optical system according to the presentinvention is incorporated into an objective optical system in a finderunit of an electronic camera. FIG. 11 is a perspective view showing theexternal appearance of an electronic camera 40 as viewed from the frontside thereof. FIG. 12 is a perspective view of the electronic camera 40as viewed from the rear side thereof. FIG. 13 is a sectional viewshowing the arrangement of the electronic camera 40. In the illustratedexample, the electronic camera 40 includes a photographic optical system41 having an optical path 42 for photography, a finder optical system 43having an optical path 44 for the finder, a shutter 45, a flash 46, aliquid crystal display monitor 47, etc. When the shutter 45, which isplaced on the top of the camera 40, is depressed, photography isperformed through an objective optical system 48 for photography. Anobject image produced by the objective optical system 48 for photographyis formed on an image pickup surface 50 of a CCD 49 through a filter 51,e.g. a low-pass filter, an infrared cutoff filter, etc. The object imagereceived by the CCD 49 is processed in a processor 52 and displayed asan electronic image on the liquid crystal display monitor 47, which isprovided on the rear of the camera 40. The processor 52 is provided witha memory or the like to enable the photographed electronic image to berecorded. It should be noted that the memory may be provided separatelyfrom the processor 52. The arrangement may also be such that thephotographed electronic image is electronically recorded or written on afloppy disk or the like. The camera 40 may be arranged in the form of asilver halide camera in which a silver halide film is disposed in placeof the CCD 49.

[0238] Furthermore, an image-forming optical system similar to Example4, by way of example, is placed in the optical path 44 for the finder asan objective optical system 53 for the finder. In this case, a coverlens 54 having a negative power is provided as a cover member to form apart of the objective optical system 53, thereby enlarging the fieldangle. It should be noted that the cover lens 54 and a part of the prism10 that is closer to the object side than the stop 2 constitute a frontunit of the objective optical system 53 for the finder, and a part ofthe prism 10 that is closer to the image side than the stop 2constitutes a rear unit of the objective optical system 53 for thefinder. An object image produced by the objective optical system 53 forthe finder is formed on a view frame 57 of a Porro prism 55, which is animage-erecting member. It should be noted that the view frame 57 isplaced between a first reflecting surface 56 and second reflectingsurface 58 of the Porro prism 55. An ocular optical system 59 is placedbehind the Porro prism 55 to lead an erect image to an observer'seyeball E.

[0239] In the camera 40, which is arranged as stated above, theobjective optical system 53 for the finder can be constructed with aminimal number of optical members. Accordingly, a high-performance andlow-cost camera can be realized. In addition, because the optical pathof the objective optical system 53 can be folded, the degree of freedomwith which the constituent elements can be arranged in the cameraincreases. This is favorable for design.

[0240] Although no mention is made of the arrangement of the objectiveoptical system 48 for photography in the electronic camera 40 shown inFIG. 13, it should be noted that the objective optical system 48 forphotography may be formed by using not only a refracting coaxial opticalsystem but also any of the image-forming optical systems, whichcomprises a single prism 10, according to the present invention.

[0241]FIG. 14 is a conceptual view showing an arrangement in which animage-forming optical system according to the present invention isincorporated into an objective optical system 48 in a photography partof an electronic camera 40. In this example, an image-forming opticalsystem similar to Example 4 is used in the objective optical system 48for photography, which is placed in an optical path 42 for photography.An object image produced by the objective optical system 48 forphotography is formed on an image pickup surface 50 of a CCD 49 througha filter 51, e.g. a low-pass filter, an infrared cutoff filter, etc. Theobject image received by the CCD 49 is processed in a processor 52 anddisplayed in the form of an electronic image on a liquid crystal displaydevice (LCD) 60. The processor 52 also controls a recording device 61for recording the object image detected by the CCD 49 in the form ofelectronic information. The image displayed on the LCD 60 is led to anobserver's eyeball E through an ocular optical system 59. The ocularoptical system 59 is formed from a decentered prism having aconfiguration similar to that used in the image-forming optical systemaccording to the present invention. In this example, the ocular opticalsystem 59 has three surfaces, i.e. an entrance surface 62, a reflectingsurface 63, and a surface 64 serving as both reflecting and refractingsurfaces. At least one of the two reflecting surfaces 63 and 64,preferably each of them, is formed from a plane-symmetry free-formsurface with only one plane of symmetry that gives a power to a lightbeam and corrects decentration aberrations. The only one plane ofsymmetry is formed in approximately the same plane as the only one planeof symmetry of the plane-symmetry free-form surfaces in the prism 10provided in the objective optical system 48 for photography. Theobjective optical system 48 for photography may include another lens(positive or negative lens) as a constituent element on the object orimage side of the prism 10.

[0242] In the camera 40 arranged as stated above, the objective opticalsystem 48 for photography can be constructed with a minimal number ofoptical members. Accordingly, a high-performance and low-cost camera canbe realized. In addition, because all the constituent elements of theoptical system can be arranged in the same plane, it is possible toreduce the thickness in a direction perpendicular to the plane in whichthe constituent elements are arranged.

[0243] Although in this example a plane-parallel plate is placed as acover member 65 of the objective optical system 48 for photography, itis also possible to use a lens having a power as the cover member 65 asin the case of the above-described example.

[0244] The surface closest to the object side in the image-formingoptical system according to the present invention may be used as a covermember instead of providing a cover member separately. In this example,the entrance surface of the prism 10 is the closest to the object sidein the image-forming optical system. In such a case, however, becausethe entrance surface is decentered with respect to the optical axis, ifthis surface is placed on the front side of the camera, it gives theillusion that the photographic center of the camera 40 is deviated fromthe subject when the entrance surface is seen from the subject side (thesubject normally feels that photographing is being performed in adirection perpendicular to the entrance surface, as in the case ofordinary cameras). Thus, the entrance surface would give a sense ofincongruity. Therefore, in a case where the surface of the image-formingoptical system that is closest to the object side is a decenteredsurface as in this example, it is desirable to provide the cover member65 (or cover lens 54) from the viewpoint of preventing the subject fromfeeling incongruous when seeing the entrance surface, and allowing thesubject to be photographed with the same feeling as in the case of theexisting cameras.

[0245]FIG. 15 is a conceptual view showing an arrangement in which animage-forming optical system according to the present invention isincorporated into an objective optical system 81 in an observationsystem of a video endoscope system. In this case, the objective opticalsystem 81 in the observation system uses an image-forming optical systemapproximately similar to Example 3. As shown in part (a) of FIG. 15, thevideo endoscope system includes a video endoscope 71, a light sourceunit 72 for supplying illuminating light, a video processor 73 forexecuting processing-of signals associated with the video endoscope 71,a monitor 74 for displaying video signals output from the videoprocessor 73, a VTR deck 75 and a video disk 76, which are connected tothe video processor 73 to record video signals and so forth, and a videoprinter 77 for printing out video signals in the form of images. Thevideo endoscope system further includes a head-mounted image displayapparatus (HMD) 78. The video endoscope 71 has an insert part 79 with adistal end portion 80. The distal end portion 80 is arranged as shown inpart (b) of FIG. 15. A light beam from the light source unit 72 passesthrough a light guide fiber bundle 87 and illuminates a part to beobserved through an objective optical system 86 for illumination. Lightfrom the part to be observed enters an objective optical system 81 forobservation through a cover member 85. Thus, an object image is formedby the objective optical system 81. The object image is formed on animage pickup surface 84 of a CCD 83 through a filter 82, e.g. a low-passfilter, an infrared cutoff filter, etc. Furthermore, the object image isconverted into a video signal by the CCD 83. The video signal isdisplayed directly on the monitor 74 by the video processor 73, which isshown in part (a) of FIG. 15. In addition, the video signal is recordedin the VTR deck 75 and on the video disk 76 and also printed out in theform of an image from the video printer 77. In addition, the objectimage is displayed on the image display device of the HMD 78, therebyallowing a person wearing the HMD 78 to observe the displayed image.

[0246] The endoscope arranged as stated above can be constructed with aminimal number of optical members. Accordingly, a high-performance andlow-cost endoscope can be realized. Moreover, because the constituentportions of the single prism 10 of the objective optical system 81 inthe observation system are arranged in series in the direction of thelongitudinal axis of the endoscope, the above-described advantageouseffects can be obtained without hindering the achievement of a reductionin the diameter of the endoscope.

[0247] Incidentally, the image-forming optical system can also be usedas a projection optical system by reversing the optical path. FIG. 16 isa conceptual view showing an arrangement in which a prism optical systemaccording to the present invention is used in a projection opticalsystem 96 of a presentation system formed by combining together apersonal computer 90 and a liquid crystal projector 91. In this example,an image-forming optical system similar to Example 1 except that theoptical path is reverse to that in Example 1 is used in the projectionoptical system 96. Referring to FIG. 16, image and manuscript dataprepared on the personal computer 90 is branched from a monitor outputand delivered to a processing control unit 98 in the liquid crystalprojector 91. In the processing control unit 98 of the liquid crystalprojector 91, the input data is processed and output to a liquid crystalpanel (LCP) 93. The liquid crystal panel 93 displays an imagecorresponding to the input image data. Light from a light source 92 isapplied to the liquid crystal panel 93. The amount of light transmittedby the liquid crystal panel 93 is determined by the gradation of theimage displayed on the liquid crystal panel 93. Light from the liquidcrystal panel 93 is projected on a screen 97 through a projectionoptical system 96 comprising a field lens 95 placed immediately in frontof the liquid crystal panel 93, a prism 10 constituting theimage-forming optical system according to the present invention, and acover lens 94 which is a positive lens.

[0248] The projector arranged as stated above can be constructed with aminimal number of optical members. Accordingly, a high performance andlow-cost projector ran be realized. In addition, the projector can beconstructed in a compact form.

[0249]FIG. 17 is a diagram showing a desirable arrangement for theimage-forming optical system according to the present invention when theimage-forming optical system is placed in front of an image pickupdevice, e.g. a CCD, or a filter. In the figure, a decentered prism P isa prism included in the image-forming optical system according to thepresent invention. When the image pickup surface D of an image pickupdevice forms a quadrangle as shown in the figure, it is desirable fromthe viewpoint of forming a beautiful image to place the decentered prismP so that the plane F of symmetry of a plane-symmetry free-form surfaceprovided in the decentered prism P is parallel to at least one of thesides forming the quadrangular image pickup surface D.

[0250] When the image pickup surface D has a shape in which each of thefour interior angles is approximately 90 degrees, such as a square or arectangle, it is desirable that the plane F of symmetry of theplane-symmetry free-form surface should be parallel to two sides of theimage pickup surface D that are parallel to each other. It is moredesirable that the plane F of symmetry should lie at the middle betweentwo parallel sides and coincide with a position where the image pickupsurface D is in a symmetry between the right and left halves or betweenthe upper and lower halves. The described arrangement enables therequired assembly accuracy to be readily obtained when the image-formingoptical system is incorporated into an apparatus, and is useful formass-production.

[0251] When a plurality or all of the optical surfaces constituting thedecentered prism P, i.e. the entrance surface, the first reflectingsurface, the surface C, the surface B, the surface A, and so forth, areplane-symmetry free-form surfaces, it is desirable from the viewpoint ofdesign and aberration correcting performance to arrange the decenteredprism P so that the planes of symmetry of the plurality or all of theoptical surfaces are in the same plane F. In addition, it is desirablethat the plane F of symmetry and the image pickup surface D should be inthe above-described relationship.

[0252] As will be clear from the foregoing description, the presentinvention makes it possible to provide a high-performance and low-costimage-forming optical system with a minimal number of constituentoptical elements. In addition, it is possible to provide ahigh-performance image-forming optical system that is made compact andthin by folding an optical path using reflecting surfaces arranged tominimize the number of reflections.

1-29. (canceled).
 30. An image projector for projecting a real imageonto a screen, said image projector comprising: a light source; anoptical system including at least a lens and a plurality of reflectingsurfaces; and a display for image display; wherein said optical systemincludes an M-shaped folded light path formed by said plurality ofreflecting surfaces, and one of said reflecting surfaces is arotationally asymmetric aspherical surface.
 31. An image projectoraccording to claim 30, wherein said optical system includes threereflecting surfaces, and when said reflecting surfaces are defined as afirst reflecting surface, a second reflecting surface, and a thirdreflecting surface in order from a side closer to said display, thesereflecting surfaces are positioned so that a line connecting a point ofreflection on the first reflecting surface, a point of reflection on thesecond reflecting surface and a point of reflection on the thirdreflecting surface does not intersect itself.
 32. An image projectoraccording to claim 31, wherein of said plurality of reflecting surfaces,at least one of the two reflecting surfaces closer to said display asviewed along the light path is a rotationally asymmetric asphericalsurface.
 33. An image projector according to claim 32, wherein anincident angle αc of an axial principal ray on the reflecting surfaceclosest to said display satisfies the following condition: 5°<αc<45°.34. An image projector according to claim 33, wherein the incident angleαc of the axial principal ray on the reflecting surface closest to saiddisplay satisfies the following condition: 10°<αc<40°.
 35. An imageprojector according to claim 33, wherein the incident angle αc of theaxial principal ray on the reflecting surface closest to said displaysatisfies the following condition: 20°<αc<30°.
 36. An image projectoraccording to claim 32, wherein the incident angle αb of the axialprincipal ray on the reflecting surface second closest to said displaysatisfies the following condition: 5°<αb<45°.
 37. An image projectoraccording to claim 36, wherein the incident angle αb of the axialprincipal ray on the reflecting surface second closest to said displaysatisfies the following condition: 10°<αb<40°.
 38. An image projectoraccording to claim 36, wherein the incident angle αb of the axialprincipal ray on the reflecting surface second closest to said displaysatisfies the following condition: 20°<αb<30°.
 39. An image projectoraccording to claim 32, wherein an incident angle αc of an axialprincipal ray on a reflecting surface closest to said display and anincident angle αb of the axial principal ray on a reflecting surfacesecond closest to said display satisfy the following conditions:5°<αc<45°5°<αb<45°.
 40. An image projector according to claim 32,wherein an incident angle αc of an axial principal ray on a reflectingsurface closest to said display and an incident angle αb of the axialprincipal ray on a reflecting surface second closest to said displaysatisfy the following conditions: 10°<αc<40°10°<αb<40°.
 41. An imageprojector according to claim 40, wherein the incident angle αc of theaxial principal ray on the reflecting surface closest to said displayand the incident angle αb of the axial principal ray on the reflectingsurface second closest to said display satisfy the following condition:0.6<αbc=αc/αb<1.4.
 42. An image projector according to claim 41, whereinthe incident angle αc of the axial principal ray on the reflectingsurface closest to said display and the incident angle αb of the axialprincipal ray on the reflecting surface second closest to said displaysatisfy the following condition: 0.8<αbc<1.2.
 43. An image projectoraccording to claim 41, wherein the incident angle αc of the axialprincipal ray on the reflecting surface closest to said display and theincident angle αb of the axial principal ray on the reflecting surfacesecond closest to said display satisfy the following condition:0.9<αdc<1.1.
 44. An image projector according to claim 30, which has alens in a window through which light emerges from said projector toproject an image onto the screen.
 45. An image projector according toclaim 31, wherein a lens is positioned in an entrance-side light pathentering said optical system, and another lens is positioned in anexit-side light path exiting from said optical system.
 46. An imageprojector according to claim 31, wherein said first reflecting surfaceand said third reflecting surface are connected to each other with astep interposed therebetween.
 47. An image projector according to claim32, wherein said rotationally asymmetric aspherical surface has only oneplane of symmetry.
 48. An image projector according to claim 30, whereinsaid rotationally asymmetric aspherical surface is decentered and has astrong curvature in a positive direction of a Y-axis and a weakcurvature in a negative direction of the Y-axis.
 49. An image projectoraccording to claim 32, wherein said rotationally asymmetric asphericalsurface is decentered and has a strong curvature in a positive directionof a Y-axis and a weak curvature in a negative direction of the Y-axis.50. A catadioptric system comprising: at least one lens; and at leastthree reflecting surfaces; wherein when said three reflective surfacesare defined as a first (B) reflecting surface, a second (C) reflectingsurface, and a third (11) reflective surface in order along a lightpath, these reflecting surfaces are positioned so that a line connectinga point of reflection on the first reflecting surface, a point ofreflection on the second reflecting surface and a point of reflection onthe third reflecting surface does not intersect itself; at least one ofthe said first and second reflecting surfaces being a rotationallysymmetric aspherical surface; said first reflecting surface and saidthird reflecting surface being connected to each other with a stepinterposed therebetween; said first reflecting surface and said thirdreflecting surface facing approximately in a same direction; and whereina lens is positioned in an entrance-side light path entering areflecting optical system formed from said three reflecting surfaces,and another lens is positioned in an exit-side light path exiting fromsaid reflecting optical system.